Question

X~N(0,1)

What is the distribution of X^2 and X^(-2)?

Thank you:)

Answer #1

1. Suppose X~N(0,1), what is Pr (X< -1.96)
2. Suppose X~N(0,1), what is Pr (1.20 <X<1.96)
3. Suppose X~N(0,1), what is Pr ( -1.96<X< 1.20)
Please use step by step work. I'm struggling to grasp the
concepts. Thank you.

1. Suppose X~N(0,1), what is Pr (0<X<1.20)
2. Suppose X~N(0,1), what is Pr (0<X<1.96)
3. Suppose X~N(0,1), what is Pr (X<1.96)
4. Suppose X~N(0,1), what is Pr (X> 1.20)
Please use step by step work. I'm struggling with grasping the
process. Thank you.

Let X and Y be independent N(0,1) RVs. Suppose U =
(X+Y)/squareroot(2) and V = (X-Y)/squareroot(2).
Please derive the joint distribution of (U, V ) by using the
Jacobian matrix method.

Let N have a Poisson distribution with parameter lander=1.
Conditioned on N=n,
let X have a uniform distribution over the integers
0,1,.......,n+1. What is the
marginal distribution for X?
Step by step and show what definition you use

Suppose X ~ N(0,1).
a.) Derive the expression of cdf F(x) for X^2
b.) Find the numerical value of F(2)

PLEASE SHOW DETAILED STEPS. THANK YOU.
1. A random variable X has a normal distribution N(5,3.5). Find
P(X>0) Show the calculator input for your answer.
2. Let X~Binomial(9,0.6). Find P(X≥5) Show the calculator input
for your answer.

Suppose (Z1, Z2) is a bivariate Gaussian pair of random
variables with Z1 ~ N (0,1), Z2 ~ (0,1) and cov (Z1, Z2) = -0.5.
Find P (Z2 >2 | Z1=-2). The answer is 0.1241. Can you explain
why? Thank you.

Show that if X ∼ N(0,1) and Y ∼ chi-squares with df n are
independent, X/sqrt(Y/n) is Student t with df n.

Prove that |R^2| = |R| by showing |(0,1) x (0,1)| = |(0,1)| through
cardinality.

If X ~ N (3, 2²) and Y ~ N(1, 2²) what is the distribution of 2X-Y??
please show all the step.

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