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A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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If X(n,p) is a binomial random variable with parameters n and p, then why is it that X(n+1,p) stochastically dominates X(n,p)?
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- The executives at a software company called Front Line are trying to decide if they should continue to provide free coffee in their breakrooms. They have 79 employees and each employee has a 67% chance of drinking coffee in the break room each day. Recall, for a binomial random variable, dbinom(j,n,p) = P(Y= j) and pbinom(j,n,p) = P(Y< j). What is the probability that more than 20 employees will drink coffee in one day?arrow_forwardObtain the expected value of a random variable with four values 1,2,3,4 with probabilities P(1)= 1/4 ; P(2)=1/4 ; P(3)=1/8 ; P(4)=3/8arrow_forwardLet Y be a binomial random variable with n = 10 and p = 0.3. (a) P(3 < Y < 5) = P(3 ≤ Y < 5) = (b) P(3 < Y ≤ 5) = P(3 ≤ Y ≤ 5) =arrow_forward
- A nuclear reactor becomes unstable if both safety mechanisms A and B fail. The probabilities of failure are P(A) =1/300 and P(B) = 1/200. Also, if A has failed, B is then more likely to fail: P(B/A)=1/100. a) What is the probability of the reactor going unstable? b) If B has failed, what is the probability of the reactor going unstable?arrow_forwardI asked this question (If X(n,p) is a binomial random variable with parameters n and p, then why is it that X(n+1,p) stochastically dominates X(n,p)?) this morning and got a response which was fine--no complaints about that! But, I was wondering if the question could be answered without showing a formal proof, but rather just by a verbal-type of explanation? I was thinking something along these lines: X(n+1,p) stochastically dominates X(n,p) since the expected value of X(n+1,p)=(n+1)p is greater than the expected value of X(n,p)=np, and X(n+1,p) and X(n,p) are increasing functions. Let me know if this makes sense or needs revision. Thanks for the help. I appreciate it.arrow_forwardIf Xis a random variable having a binomial distributionwith n = 20 and p = 0.4, and Y is a transformed version of X,where Y = 2X + 3, what is the expected value of Y?arrow_forward
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