Question

In: Statistics and Probability

Probability: Y is a normal random variable with ? = 0 and ?^2 = 1. SOLVE...

Probability:

Y is a normal random variable with ? = 0 and ?^2 = 1.

SOLVE FOR expectation E[Y] and variance Var(Y).

Solutions

Expert Solution

Here, our random variable Y is a Standard Normal Random Variable.

We have to solve for E(Y) and Var(Y).

The detailed procedure to answer the given question is as given in the images below:-

Hence, E(Year)= 0 and Var(Y)=1

This answers your question.

If you have understood the answer please rate Positively.


Related Solutions

Use R to compute the probability that a Normal random variable with mean 0 and variance...
Use R to compute the probability that a Normal random variable with mean 0 and variance 3.7 is less than.2. Find the 93% quantile of the above random variable by using the R command and also by using the z -table.
Solve the differential equation y''+y'-2y=3, y(0)=2, y'(0) = -1
Solve the differential equation y''+y'-2y=3, y(0)=2, y'(0) = -1
solve by details y"+y=-1 ,y(0)=0,y(Pi/2)=0 by properties of green function
solve by details y"+y=-1 ,y(0)=0,y(Pi/2)=0 by properties of green function
What is the probability that a normal random variable with mean 2 and standard deviation 4...
What is the probability that a normal random variable with mean 2 and standard deviation 4 will be less than 3?
1- Use Heun’s method without iteration to solve ?2???2−0.5?+?=0 y(0) = 2 and y’(0) = 0...
1- Use Heun’s method without iteration to solve ?2???2−0.5?+?=0 y(0) = 2 and y’(0) = 0 solve from x = 0 to 3 using h = 0.2 (step size) present y values as a table versus x values (50p) Instructions about question 1: considering step size and interval for x it will not be reasonable to proceed through hand calculations. You may want to use excel or other software but you need to write down first 3 steps of the...
The following table provides a probability distribution for the random variable y. y f(y) 2 0.10...
The following table provides a probability distribution for the random variable y. y f(y) 2 0.10 4 0.20 7 0.40 9 0.30 a. Compute E(y) (to 1 decimal). b. Compute Var(y) and ? (to 2 decimals). Var(y) ?
QUESTION 1 If Z is a standard normal random variable, then P(Z > 0) =   0...
QUESTION 1 If Z is a standard normal random variable, then P(Z > 0) =   0 1 0.4579 0.5 1 points    QUESTION 2 Company A claims that 20% of people in Sydney prefer its product (Brand A). Company B disputes the 20% but has no idea whether a higher or lower proportion is appropriate.  Company B randomly samples 400 people and 88 of them prefer Company A's product (Brand A). Assuming a 5% significance level, which one of the following...
2. Let X be a uniform random variable over the interval (0, 1). Let Y =...
2. Let X be a uniform random variable over the interval (0, 1). Let Y = X(1-X). a. Derive the pdf for Y . b. Check the pdf you found in (a) is a pdf. c. Use the pdf you found in (a) to find the mean of Y . d. Compute the mean of Y by using the distribution for X. e. Use the pdf of Y to evaluate P(|x-1/2|<1/8). You cannot use the pdf for X. f. Use...
1. solve the IVP: xy''-y/x=lnx, on (0, inifnity), y(1)=-1, y'(1)=-2 2.solve the IVP: y''-y=(e^x)/sqrtx, y(1)=e, y'(1)=0...
1. solve the IVP: xy''-y/x=lnx, on (0, inifnity), y(1)=-1, y'(1)=-2 2.solve the IVP: y''-y=(e^x)/sqrtx, y(1)=e, y'(1)=0 3. Given that y1(x)=x is a solution of xy''-xy'+y=0 on (0, inifinity, solve the IVP: xy''-xy'+y=2 on(0,infinity), y(3)=2, y'(3)=1 14. solve the IVP: X'=( 1 2 3) X, X(0)=(0 ##################0 1 4####### -3/8 ##################0 0 1 ########1/4
Find the general solution and solve the IVP y''+y'-y=0, y(0)=2, y'(0)=0
Find the general solution and solve the IVP y''+y'-y=0, y(0)=2, y'(0)=0
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT