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[20] A plant sheds X seeds, where X B(n,p).Each seed germinates with probability o independently of...
(c) Idifficult] Let x ~ Binomial (n, p) where n is an even number. Find the PMF of Y g(X) mod (X, 2) where "mod" denotes modulus division of the first argument by the second argument (d) Idifficult MA] Let X~NegBin (k, p). Find the PMF of Y g(X) = mod(X, n) where n E N
H.W. #5 - Q #8:
8. Suppose that n-48 seeds are planted and suppose that each seed has a probability p 75% of germinating. Let X be the number of seeds that germinate and use the Central Limit Theorem to estimate the probability P(35 < X < 40) that between 35 and 40 seeds germinate. Don't forget to use a continuity correction.
2. (a) Given that N-n, the conditional distribution of Y is x The unconditional distribution of N is Poisson (8). Calculate E(Y) and Var(Y). (b) A plant supervisor is interested in budgeting weekly repair costs for a certain type of machine. Records over the past years indicate that these repair cost have an exponential distribution with mean 20 for each machine studied. Let Y1, Y2, ..., Ysdenote the repair costs for five of these machines for the next week. Find...
3a. On a certain aircraft, the main control circuit on an autopilot fails with probability p. A redundant backup eircuit fails independently with probability q. The aircraft can fly if at least one of the circuits is functioning. Find the probability that the aircraft cannot fly. 4 pt. b. Let X and Y be the random variables with respective pmf's shown in the side figure. Compute var(X), var(Y). 23 pt. 3 pt. c. | At Problem 3-b, find the PMF...
Problem 2. Suppose a website sells X computers where X is modeled as a geometric random variable with parameter pi. Suppose that each computer is defective (i.e., needs to be returned for repair or replacement). independently with probability p2. Let Y be the mumber of computers sold which are defective. For this problem, recall that a geometric random variable X with parameter pi has pmf otherwise (a) Find ElY. (b) Find Var(Y). (c) Find P(Y 0).
1. There are times when a shifted exponential model is appropriate. That is, let the pdf of X be (a) Find the cdf of X. (b) Find the mean and variance of X. 2. Suppose X is a Gamma random variable with pdf 「(a)go Show that the moment generating function is M(t) 3, Let X equal the nurnber out of n 48 mature aster seeds that will germinate when p- 0.75 is the probability that a particular seed germinates. Approximate...
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2. (20 points) Three fair coins are flipped independently. Let X be the number of heads among the three coins. (a) Write down all possible values that X can take. (b) Construct the probability mass function of X. (c) What is the probability that we observe two or more heads. (i.e., P(X > 2)) (d) Compute E(X) and Var(X).
Questionl The random variable X and Y have the following joint probability mass function: 0.14 0.27 0.2 0.1 0.03 0.15 0.1 a) Determine the b) Find P(X-Y>2). c) Find PX s3|Y20) d) Determine E(XY) e) Determine E(X) and E(Y). f) Are X and Y independent? marginal pmf for X and Y. Question 2 Let X and Y be independent random variables with pdf 2-y 0sxS 2 f(x)- f(p)- 0, otherwise 0, otherwise a) b) Find E(XY). Find Var (2X +...
A machine produces coins such that the probability of heads, p, follows a Beta distribution with parameters (α, β) = (1, 1). A coin produced by this machine is picked at random and tossed independently n times. Let Y be the number of heads. (a) Find E[Y]. (b) Write down the pmf for Y (your answer can include unevaluated integrals and combination numbers [aka “n choose m” symbols]).
4. You toss n coins, each showing heads with probability p, independently of the other tosses. Each coin that shows tails is tossed again. Let X be the total number of tails (a) What type of distribution does X have? Specify its parameter(s). (b) What is the probability mass function of the total number of tails X?