FINAL EXAM

MTH 361 INTRODUCTION TO PROBABILITY

概率考试代写 Problem 1 (10 points).A fair die is rolled until the first time T that a six turns up. Find the conditional probability P(T > 8 | T > 4).

Problem 1 (10 points).

A fair die is rolled until the first time T that a six turns up. Find the conditional probability P(T > 8 | T > 4).

Problem 2 (10 points).  概率考试代写

Let X be a random variable normally distributed with parameters µ = 70, σ = 10. Estimate P(X > 90).

Problem 3 (10 points).  概率考试代写

A fair coin is tossed three times. Let X be the number of heads that turn up. Find E(X) and V (X).

Problem 4 (10 points).  概率考试代写

Let X be a random variable with range [−1, 1] and let fX(x) = (3/2)x2 for |x| ≤ 1 be the density function of X. Find E(X) and V (X).

Problem 5 (10 points).

Let X1 and X2 be independent random variables with common distribution

Find the distribution of the sum X₁ + X₂.

Problem 6 (10 points).

Suppose that X and Y are independent random variables with density functions

Let Z = X + Y . Find the density function fZ.