Hello. I have the following questions.

1. Let X, Y and Z be three independently and indenticallly distributed continious random variables. Find P(X<=Y<=Z)

Ans choices: (A) 1/6 (B) 1/5 (c) 1/4 (d) 1/3 (e) 1/2

2. Let X be a discrete random variable with moment generating function

M_x(t) = 1/(2-t) + summation(j = 0 ---> infinity) e^(tj-1)/(2j!)

Note: tj = t multipled by j.

Ans choices: (A) 1-e^-1 (b) 0.5(1-e^-1) (c) 1/2 + summation (j=0-->infinity)(e^(t*j-1)/2*j! (d) 0.5(1-e^-1+e^-2) (e) 1/2

3. At a party, 9 people put their hats in the center of a room where the hats are mixed together. Each person then randomly selects one hat. Denote X the number of people who select their own hat. Find Var(X)

Ans choices: (A) 4 (B) 3 (c) 2 (d) 1 (e) 0.5

4. Mary pruchases an auto insurance policy fron an insurance company which covers partial damage or total loss of her car for one year period. This policy is subject to a deductible of $1000, and a maximum payment of $10,000. During the policy year the probability o f a partial damage to Mary's car is 0.04 and the prob of total loss of her car is 0.02. If there is partial damage to her car, the amount of damage X follows a distribution with the density function

f(x) = 1/12500, xbelongs to (0,12500), 0 otherwise

Ans choices: (A) 408 (B) 410 (c) 424 (d) 450 (e) 550

For the above questions, I made strong efforts towards obtaining a solution, but I still did not obtain the answer listed in the above choices.

Any help would be greatly appreciated.

Thank you.

1. Let X, Y and Z be three independently and indenticallly distributed continious random variables. Find P(X<=Y<=Z)

Ans choices: (A) 1/6 (B) 1/5 (c) 1/4 (d) 1/3 (e) 1/2

2. Let X be a discrete random variable with moment generating function

M_x(t) = 1/(2-t) + summation(j = 0 ---> infinity) e^(tj-1)/(2j!)

Note: tj = t multipled by j.

Ans choices: (A) 1-e^-1 (b) 0.5(1-e^-1) (c) 1/2 + summation (j=0-->infinity)(e^(t*j-1)/2*j! (d) 0.5(1-e^-1+e^-2) (e) 1/2

3. At a party, 9 people put their hats in the center of a room where the hats are mixed together. Each person then randomly selects one hat. Denote X the number of people who select their own hat. Find Var(X)

Ans choices: (A) 4 (B) 3 (c) 2 (d) 1 (e) 0.5

4. Mary pruchases an auto insurance policy fron an insurance company which covers partial damage or total loss of her car for one year period. This policy is subject to a deductible of $1000, and a maximum payment of $10,000. During the policy year the probability o f a partial damage to Mary's car is 0.04 and the prob of total loss of her car is 0.02. If there is partial damage to her car, the amount of damage X follows a distribution with the density function

f(x) = 1/12500, xbelongs to (0,12500), 0 otherwise

Ans choices: (A) 408 (B) 410 (c) 424 (d) 450 (e) 550

For the above questions, I made strong efforts towards obtaining a solution, but I still did not obtain the answer listed in the above choices.

Any help would be greatly appreciated.

Thank you.

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