find the value of e(|z|), where z is a standard normal variable.
Answers
To find the value of e(|z|), where z is a standard normal variable, we first need to determine the probability density function of |z|.
Let Y = |Z|, where Z is a standard normal variable. Then:
P(Y ≤ y) = P(|Z| ≤ y) = P(-y ≤ Z ≤ y) = Φ(y) - Φ(-y)
where Φ is the cumulative distribution function of the standard normal distribution.
The probability density function of Y can be obtained by differentiating the cumulative distribution function:
f_Y(y) = d/dy (Φ(y) - Φ(-y))
= φ(y) + φ(-y)
= 2φ(y)
where φ is the probability density function of the standard normal distribution.
Therefore, the expected value of |Z| is given by:
E(|Z|) = ∫₀^∞ y f_Y(y) dy
= 2 ∫₀^∞ y φ(y) dy
= 2 ∫₀^∞ (1/√(2π)) y e^(-y²/2) dy (using the standard normal density function)
This integral can be evaluated using integration by substitution, with u = y²/2 and du/dy = y. Thus:
E(|Z|) = 2 ∫₀^∞ (1/√(2π)) e^(-u) du
= 2/√(2π) * [ -e^(-u) ]_0^∞
= 2/√(2π)
= √(2/π)
Therefore, e(|z|) = √(2/π) ≈ 0.7979.
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Related Questions
Of fixed-rate, percentage, and triple net leases, which makes financial planning easiest for a business owner?
A:fixed-rate
B:Percentage
C:Triple net
Answers
The option that makes financial planning easiest for a business owner is: A: Fixed rate.
What is fixed rate?Fixed rate can be defined as the interest rate charge on loan and does not varies or change but remain the same.
Fixed rate is of paramount as it makes financial planning easiest for a business owner based on the fact that the interest rate does not change.
Therefore the option that makes financial planning easiest for a business owner is: A: Fixed rate.
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Why is 2020 edge so hard and annoying here is 14 points
Answers
Answer:
ty
Step-by-step explanation:
thanks for points have a good day sir
Answer:
ik right ughh
Step-by-step explanation:
Please help! (look at the image below!!)
Answers
The numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾. The third option is correct.
What is ordering of numbersThe ordering of numbers refers to arranging numbers in a specific sequence based on their magnitude or value. The ordering of numbers is determined by their relative values. Comparisons are made between numbers to determine their position in the order.
12⅝ = 101/8 = 12.645
12.62 = 12.62
√146 = 12.0830
12.39 = 12.39
12¾ = 51/4 = 12.75
Therefore, the numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾.
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25% of a population have pets. What is the probability that the next person you speak to has pets?
Answers
Answer: I d k
Step-by-step explanation:
Answer:
25
explanation:
just because
katherine gives piano lessons for $15 per hour. she also grows flowers, which she arranges and sells at the local farmer’s one day she spends 5 hours planting $50 worth of seeds in her garden. once the seeds have grown into flowers, she can sell them for $150 at the farmer’s market. katherine’s accounting profits are
Answers
Katherine will make a profit of $100.
To calculate the profit, we need to calculate the total revenue and the total cost. The total cost includes the cost of growing flowers, and the total revenue includes the amount from selling the flowers as well as the money made from piano lessons.The total cost is given by the sum of the cost of planting seeds and growing flowers.
Cost of planting seeds = $50
Total hours spent in planting seeds = 5
Cost of growing flowers = 0 (because the problem doesn’t state how much it costs to grow flowers)
Total Cost = Cost of planting seeds = $50
Total Revenue:The total revenue is given by the sum of the money earned from selling the flowers and the money earned from giving piano lessons.
Money earned from selling flowers = $150
Money earned from piano lessons = 0 (because it is not mentioned in the problem)
Total Revenue = Money earned from selling flowers = $150
Profit:Total profit is given by the difference between total revenue and total cost.
Profit = Total Revenue - Total Cost = $150 - $50 = $100
Therefore, A profit of $100 is made by Katherine.
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eight ponds of potatoes cost $3.75. How much will 20 pounds cost?
Answers
Answer:
$9.38
Step-by-step explanation:
First, we have to find how much a single pound of potato costs.
3.75 / 8 = 0.46875
Since we know the cost of one pound, simply multiply it by 20 to find the cost of 20 pounds of potatoes.
0.46875 * 20 = 9.375
Answer:
$15.20
Step-by-step explanation:
first you must find the cost of each potato per pound, which will be 76 cents per pound then you multiply by 20 and u get 15.2 which is the answer
pls brainelist if this helps
∞(PLEASE HURRY)
On a coordinate plane, a line segment contains points (negative 4, 4) and (4, 2). Another line segment contains points (negative 2, 2) and (2, 1).
The ordered pair (–4, 4) is on the pre-image. A scale factor was applied to produce the image on the coordinate plane.
What is the scale factor?
1/4
1/2
2
4
Answers
Answer:
1/2
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
an experimenter flips a coin 100 times and gets 34 heads. test the claim that the coin is fair against the two-sided claim that it is not fair at the level α=.01.
Answers
Based on the results of the hypothesis test, we reject the claim that the coin is fair and accept the alternative hypothesis that the coin is not fair.
To test the claim that the coin is fair against the two-sided claim that it is not fair, we can use a hypothesis test. The null hypothesis (H0) assumes that the coin is fair, and the alternative hypothesis (H1) assumes that the coin is not fair.
Null hypothesis (H0): The coin is fair.
Alternative hypothesis (H1): The coin is not fair.
Given that the experimenter flipped the coin 100 times and obtained 34 heads, we can calculate the observed proportion of heads (p) in the sample:
p = 34/100 = 0.34
To conduct the hypothesis test at a significance level of α = 0.01, we will use the chi-square test statistic. The test statistic is calculated as follows:
χ² = (observed - expected)² / expected
For a fair coin, the expected probability of getting a head is 0.5, and the expected number of heads in 100 flips would be:
expected = 0.5 * 100 = 50
Now, let's calculate the chi-square test statistic:
χ² = (34 - 50)² / 50 + (66 - 50)² / 50
= (-16)² / 50 + (16)² / 50
= 256 / 50 + 256 / 50
= 5.12 + 5.12
= 10.24
The degrees of freedom (df) for this test are df = 1 (since we have two possible outcomes: heads or tails) and the critical value for a two-sided test at α = 0.01 with df = 1 is approximately 6.63.
Since the test statistic (10.24) is greater than the critical value (6.63), we reject the null hypothesis (H0) at the α = 0.01 level. We have sufficient evidence to conclude that the coin is not fair.
Therefore, based on the results of the hypothesis test, we reject the claim that the coin is fair and accept the alternative hypothesis that the coin is not fair.
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I need help pleaseeeee
Answers
The line equation which models the data plotted on the graph is y = -16.67X + 1100
The equation for the line of best fit is expressed by the relation :
y = bx + cb = slope ; c = intercept
The slope , b = (change in Y/change in X)
Using the points : (28, 850) , (40, 650)
slope = (850 - 650) / (28 - 40)
slope = -16.67
The intercept is the point where the best fit line crosses the y-axis
Hence, intercept is 1100
Line of best fit equation :
y = -16.67X + 1100Therefore , the equation of the line is y = -16.67X + 1100
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What is ¾ divided by ½?
Answers
When we divide 3 / 4 by 1 / 2 we get 3 / 2.
The given number to be divided is 3 / 4.
The given divisor is 1 / 2.
When we divide 3 / 4 by 1 / 2, we are supposed to multiply 3 / 4 by the reciprocal of 1 / 2 which is 2 / 1.
When we multiply 3 / 4 by 2 / 1 we get 3 / 2 as the final answer.
Thus, When we divide the given number 3 / 4 by 1 / 2 which is the given divisor we get 3 / 2 as the final answer.
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C(x)=25.50-0.20x
How much credit is left on the card after kala uses it for 15 minutes of calls?
Answers
There will be a $22.50 credit left on the card after Kala uses it for 15 minutes of calls.
We have,
The given function C(x) represents the credit remaining on a phone card after x minutes of use, where x is the number of minutes used and C(x) is the remaining credit in dollars.
C(x) = 25.50 - 0.20x
To find how much credit is left on the card after Kala uses it for 15 minutes of calls, we need to evaluate C(15).
C(15) = 25.50 - 0.20(15)
C(15) = 25.50 - 3
C(15) = 22.50
Therefore,
There will be a $22.50 credit left on the card after Kala uses it for 15 minutes of calls.
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Pls help find The value of x of the polygon
Answers
Answer:
97°
Step-by-step explanation:
First, find the sum of the interior angles by using the following formula.
\(S = (n-2)180\)
S is the sum and n is the number of sides
S = (5 - 2)180
S = (3)180
S = 540°
Next create an equation by adding all the interior angles together and setting the sum equal to the sum of the interior angles and solve for x, the missing angle.
72 + 136 + 127 + 108 + x = 540
443 + x = 540
443 - 443 + x = 540 - 443
x = 97°
write the sum in sigma notation. 3 − 3x 3x2 − 3x3 · · · (−1)n3xn
Answers
Hi! I'd be happy to help you write the sum in sigma notation. Given the sum: 3 - 3x + 3x^2 - 3x^3 + , + (-1)^n * 3x^n, the sigma notation would be:
Σ[(-1)^k * 3x^k] from k=0 to n
Here's a step-by-step explanation:
1. Identify the pattern in the sum: It alternates between positive and negative terms, and each term has a power of x multiplied by 3.
2. Assign the variable k for the index of summation.
3. Determine the range of k: The sum starts with k=0 and goes up to k=n.
4. Represent the alternating sign using (-1)^k.
5. Combine all components to form the sigma notation: Σ[(-1)^k * 3x^k] from k=0 to n.
The sum can be written in sigma notation as:
\($\displaystyle\sum_{n=1}^\infty (-1)^n 3x^n$\)
How to write sum in sigma notation?The given series is:
\(3 - 3x + 3x^2 - 3x^3 + ...\)
To write it in sigma notation, we first notice that the terms alternate in sign, and each term is a power of x multiplied by a constant (-3). We can write the general term of the series as:
\((-1)^n * 3 * x^n\)
where n is the index of the term, starting from n = 0 for the first term.
Using sigma notation, we can express the sum of the series as:
\($\displaystyle\sum_{n=1}^\infty (-1)^n 3x^n$\)
where the summation is over all values of n starting from n = 0.
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Consider the following exponential probability density function. f(x) = 1/3 4 e^-x/3 for x > 0 a. Write the formula for P(x < x_0). b. Find P(x < 2). c. Find P(x > 3). d. Find P(x < 5). e. Find P(2 <.x <5).
Answers
The probability that x is less than 2 is approximately 0.4866. The probability that x is greater than 3 is approximately 0.3528. The probability that x is less than 5 is approximately 0.6321. The probability that x is between 2 and 5 is approximately 0.1455.
The given probability density function is an exponential distribution with a rate parameter of λ = 1/3. The formula for P(x < x_0) is the cumulative distribution function (CDF) of the exponential distribution, which is given by:
F(x_0) = ∫[0,x_0] f(x) dx = ∫[0,x_0] 1/3 * 4 * e^(-x/3) dx
a. Write the formula for P(x < x_0):
Using integration, we can solve this formula as follows:
F(x_0) = [-4e^(-x/3)] / 3 |[0,x_0]
= [-4e^(-x_0/3) + 4]/3
b. Find P(x < 2):
To find P(x < 2), we simply substitute x_0 = 2 in the above formula:
F(2) = [-4e^(-2/3) + 4]/3
≈ 0.4866
Therefore, the probability that x is less than 2 is approximately 0.4866.
c. Find P(x > 3):
To find P(x > 3), we can use the complement rule and subtract P(x < 3) from 1:
P(x > 3) = 1 - P(x < 3) = 1 - F(3)
= 1 - [-4e^(-1) + 4]/3
≈ 0.3528
Therefore, the probability that x is greater than 3 is approximately 0.3528.
d. Find P(x < 5):
To find P(x < 5), we simply substitute x_0 = 5 in the above formula:
F(5) = [-4e^(-5/3) + 4]/3
≈ 0.6321
Therefore, the probability that x is less than 5 is approximately 0.6321.
e. Find P(2 < x < 5):
To find P(2 < x < 5), we can use the CDF formula to find P(x < 5) and P(x < 2), and then subtract the latter from the former:
P(2 < x < 5) = P(x < 5) - P(x < 2)
= F(5) - F(2)
= [-4e^(-5/3) + 4]/3 - [-4e^(-2/3) + 4]/3
≈ 0.1455
Therefore, the probability that x is between 2 and 5 is approximately 0.1455.
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12x — 8 = 3x + 64; x =
Answers
Answer:
x= 8
Step-by-step explanation:
12x - 8 = 3x + 64
12x - 3x = 64 + 8
9x = 72
x= 72÷9
x = 8
Answer:
x=8
Step-by-step explanation:
12x-8=3x+64 ( collect like terms)
=12x-3x=64+8 (add or subs like terms)
=9x=72 (divided both sign by 9)
=9x/9=72/9=8
x=8
i. The uniform probability distribution's shape is a rectangle. ii. The uniform probability distribution is symmetric about the mode. iii. In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values. Multiple Choice (ii) and, (iii) are correct statements but not (i). (i). (ii), and (iii) are all false statements. (i) is a correct statement but not (ii) or (iii). (i) and, (iii) are correct statements but not (ii).
Answers
The correct option is: (i) and (iii) are correct statements but not (ii).
The correct answer is:
(i) The uniform probability distribution's shape is a rectangle.
(ii) The uniform probability distribution is symmetric about the mode.
(iii) In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values.
Therefore, the correct option is: (i) and (iii) are correct statements but not (ii).
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3. Where does solar energy come from?
Enter your answer
Answers
Answer: sun
Step-by-step explanation:
cause I said
b) James went to Black Rock coffee shop and ordered
2 coffees and 5 bagels for which he paid $24. The next
morning he returned to buy 3 coffees and 4 bagels for
$22. Based on this information, determine how much
each item costs.
Answers
Answer:
Coffees cost $2 each and bagels cost $4 each
Step-by-step explanation:
Let
Coffee=c
Bagels= b
2 coffees and 5 bagels for which he paid $24
2c + 5b= 24 (1)
he returned to buy 3 coffees and 4 bagels for
$22
3c + 4b = 22 (2)
2c + 5b= 24 (1)
3c + 4b = 22 (2)
Multiply (1) by 3 and (2) by 2
6c + 15b = 72 (3)
6c + 8b = 44 (4)
Subtract (4) from (3)
15b - 8b = 72 - 44
7b = 28
Divide both sides by 7
b= 28 / 7
= 4
b= $4
Substitute b=4 into (1)
2c + 5b= 24
2c + 5(4) = 24
2c + 20 = 24
2c = 24 - 20
2c = 4
Divide both sides by 2
c= 4 / 2
c= $2
Therefore,
Coffees cost $2 each and bagels cost $4 each
Write your answer as a fraction or as a whole or mixed number
Answers
Answer:
87 2/10 km^2. hope it's helpful
Step-by-step explanation:
area = l X w
= 8 km X 10 9/10 km
= 8 X 109/ 10 km^2
= 872/10 km^2
mario has $759.60 in the bank after 2 years. assuming he made no additional deposits or withdrawls, what simple interest rate did the savings account pay?
Answers
The savings account paid a simple interest rate of 25.96%.
We can use the simple interest formula:
I = Prt
where I is the interest earned, P is the principal (initial amount deposited), r is the interest rate (in decimal form), and t is the time (in years).
The interest earned in 2 years is:
I = 759.60 - 500 = 259.60
Substituting the values into the formula, we get:
259.60 = 500 × r × 2
Simplifying and solving for r, we get:
r = 0.2596 or 25.96%
Therefore, the savings account paid a simple interest rate of 25.96%.
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mario has $759.60 in the bank after 2 years. assuming he made no additional deposits or withdrawls, what simple interest rate did the savings account pay? The initial amount deposited is $500
625=5^(7x-3) what is x
Answers
\(625=5^{7x-3}\implies 5^4=5^{7x-3}\implies 4=7x-3 \\\\\\ 7=7x\implies \cfrac{7}{7}=x\implies 1=x\)
Which statement BEST describes the equation below?
f(x) = 2x + 3
A) It is a relation
B) It is a function
C) It is a one-to-one function
Answers
Answer: function
Step-by-step explanation: I'm not totally sure so I hope this helps
Winning the jackpot in a particular lottery requires that you select the correct three numbers between 1 and 44 and , in a separate drawing, you must also select the correct single number between 1 and 41. Find the probability of winning the jackpot.
Answers
Answer:
\(\frac{1}{3,492,544}\)
Step-by-step explanation:
Since winning the lottery as described in the question is a series of events that need to occur in a sequence in order for it to be a winning ticket then this is a dependent event. Therefore to find the probability of actually winning we multiply the probability of getting each number which is calculated by dividing the amount of times the number appears by the total amount of numbers.
For example the first three numbers are 1 out of 44 therefore the probability of hitting just one correct number is \(\frac{1}{44}\) ... now we multiply
\(\frac{1}{44} * \frac{1}{44} * \frac{1}{44} * \frac{1}{41} = \frac{1}{3,492,544}\)
(Multiplying fractions is simply multiplying the numerators together and then the denominators together) Finally we see that the probability of actually winning the jackpot is \(\frac{1}{3,492,544}\)
Please help me with this homework
Answers
Can someone PLEASE help me out w this?!?!?????
Answers
Hi!
Here's your answer:
x=3 and y=0
I hope this helps!
Feel free to mark brailiest!
Please i need help When is the product of the square root of a prime number and a nonzero rational number a rational number?
Answers
Answer:
The product of the square root of a prime number and a nonzero rational number is a irrational number.
Step-by-step explanation:
Given that,
When is the product of the square root of a prime number and a nonzero rational number a irrational number.
We know that,
Prime number :
Prime number is that number whose has a two factor. first factor is one and second is themselves.
The square root of a prime number is irrational number.
Rational number :
Rational number is that number which is in fraction form.
For example : \(\dfrac{p}{q}\)
Here, p and q are integers
We need to proof the product of the square root of a prime number and a nonzero rational number is a rational number
Using given data
Suppose, the square root = √5
Rational number = \(\dfrac{2}{3}\)
We need to calculate the product of the square root of a prime number and a rational number
Using formula of product
\(R=P\timesQ\)
Where, P = square root of a prime number
Q= rational number
Put the value into the formula
\(R=\sqrt{5}\times\dfrac{2}{3}\)
\(R=\dfrac{2\sqrt{5}}{3}\)
Hence, The product of the square root of a prime number and a nonzero rational number is a irrational number.
Square numbers between 300 and 400
Answers
18^2=324
19^2=361
20^2=400
32,450 to the nearest thousand
Answers
a senate committee has 5 democrats, 5 republicans, and 1 independent. in how many ways can they sit around a circular table if all the members of each party all sit next to each other? (two seatings are considered equivalent if one is a rotation of the other.)
Answers
There are 7200 ways for the senate committee to sit around a circular table.
To solve this problem, we can use the formula for circular permutations: (n-1)!/d, where n is the total number of people and d is the number of ways in which they can be distinguished. In this case, n is 11 (5 democrats + 5 republicans + 1 independent) and d is 1 (since all the members of each party sit together, they are not distinguishable from one another). Plugging these values into the formula, we get
(11-1)!/1 = 10!/1 = 1098765432*1/1 = 7200.This means that there are 7200 ways for the senate committee to sit around a circular table.
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prove that there are no solutions in integers x and y to the equation 2x2 + 5y2 = 14.
Answers
The quadratic equation does not have solutions where both x and y are integers.
How to prove that there are no integer solutions for the equation?Here we have the following quadratic equation:
2x^2 + 5y^2 = 14
We want to check that we can't solve this equation with x and y integers, to see that, we can start by isolating one of the variables:
2x^2 + 5y^2 = 14
5y^2 = 14 - 2x^2
y^2 = (14 - 2x^2)/5
y = ±√((14 - 2x^2)/5)
Now, trivially:
(14 - 2x^2)/5
Is not an integer for any integer value of x, and this happens because 5 is not a factor of 14, thus, for any integer value of x the value of y that we get is non integer, then there aren't two integers that solve the quadratic equation.
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