Math 170A – Homework 3 – Due 25 October 20161. An insurance company has 1,000 policies. For each policy, there is one claim with probability 0.15% and no claim otherwise independent of other policies.(i) Write out the expression for (but no need to evaluate) the probability that there areat least 2 claims.(ii) Estimate the probability in (i).2. Let X1 and X2 be independent Poisson random variables with parameters ?1 and ?2 ,respectively. Show that X1 + X2 is a Poisson random variable with parameter ?1 + ?2 .3. Let X be the number of times two fair six sided dices need to be rolled (simultaneously)until the sum is 5. Find P(2 ? X ? 4).4. Let 0 < p < 1. Let X be a geometric random variable with parameter p and let Y be aBernoulli random variable with parameter 1 ? p. Assume that X and Y are independent.Show that XY + 1 is a geometric random variable with parameter p.5. Write out the expressions for (but no need to evaluate) the probabilities of the followingevents.(i) Head appears at least three times when six fair coins are tossed.(ii) A fair six sided dice is rolled 10 times. At least 3 of the results are 1.(iii) A fair six sided dice is rolled 5 times. Exactly 2 of the results are 1.6. Let 0 < p, q < 1. Let X be a binomial random variable with parameters (10, p) and let Ybe a Bernoulli random variable with parameter q. Assume that X and Y are independent.Find P(X + Y = 5). 1
It is our mission to promote academic success by providing students with superior research and writing, produced by exceptional writers and editors.
Our academic writers have all levels of degrees so that we can accommodate all academic levels. If you are a high school student, you will receive a personally assigned writer with at least a Bachelor’s degree in the subject field.
For any questions, feedback, or comments, we have an ethical customer support team that is always waiting on the line for your inquiries.
Phone: +1 (708)-515-4480