A cubic die is biased, so that for each integer n, 1 ≤n ≤6, the probability of the event {n} is p({n}) = 2p if n=3 or n=4 and p({n}) = p, otherwise. a) What is the expected number of times the die comes up 6, when it is rolled 32 times? b) What is the expected number of times the die must be rolled until the first 6 comes up?

A cubic die is biased, so that for each integer n, 1 ≤n ≤6, the probability of the event {n} is p({n}) = 2p if n=3 or n=4 and p({n}) = p, otherwise. a) What is the expected number of times the die comes up 6, when it is rolled 32 times? b) What is the expected number of times the die must be rolled until the first 6 comes up?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

If n letters are randomly placed in correctly addressed envelopes, prove that the probability that exactly r letters are placed in correct envelopes is given by : n - r 1 1 i 2 (-1)*; r= 1, 2, ..., n •••1 r ! k = 0 k !
Two cards are selected at random from 10 cards numbered 1 to 10. Find the probability that the sum is even if (i) the two cards are drawn together (ii) The two cards are drawn one after the other with replacement.
2. Iron bars produced by a machine can either be classified as "Good" with probability p, or "Bad" with probability q = 1- p. The quality of each iron bar produced is independent of each other. (a) Suppose there are n iron bars produced by the machine. Write down the probability that there are exactly r "Good" iron bars among the n of them for all positive integers r. (b) Suppose the machine keeps producing iron bars until k "Good" ones are obtained. Let X be the total number of iron bars produced. Show that the probability mass function of X is given by Px(x) = (x − 1) ₁² (1 - p)² -*. x=k, k +1,.... (c) In a single day, the machine produces exactly N = n iron bars, where N has mean and variance given by E(N) = a, Var(N) = 3. Let W be the total number of "Good" iron bars produced in a single day. i. Find E(W) and Var(W) in terms of p, a and 3. You can use the mean and variance of any standard distributions without proof as long as you state them clearly. ii. Determine the covariance…
An agent sells life insurance policies to five equally aged. healthy people According to recent date, the probability that a person lives in these conditions fon 30 years or more is Then the probability that after 30 years at least three people ae still living is: O 0.9915 O 0.9591 )- 0.0413 )0.9502
Suppose X~N(106,22) what is the probability P(x<114) in a decimal form?
A specific apple disease cannot be detected without dividing the apple. In a particular apple batch where the disease occurs, the probability that a random selected apple is infected is set to 0.15. 15 apples are picked random from the apple batch. What is the probability that a) none of the apples are infected. b) one or more of the apples are infected?
A law professor observed that only 20% of the students who get admitted to the freshmen class usually reached fourth year. Assuming that this is correct, find the probability that among 15 randomly selected first year students, exactly 3 students will reach fourth year?
An r-sided die with values 1, 2, ..., r is rolled 2n times and the results are placed in a sequence (a₁, a2,..., a2n). Find the probability that a₁ ≥ a2, az ≥ a4, ..., A2n-1 ≥ a2n.
1) If X~ N(100,49), find the probability P(X> 107)
If a coin is flippedn times, the probability of getting heads k times I Select] the probability of getting heads (n-k) times. The probability of getting only heads (no tails) in some number of coin flips is (Select ] * the probability of getting only heads (no tails) in twice that number of coin flips.
A cubic die is biased in such a way that for every integer n, 1 ≤ n ≤ 6, the probability of rolling n is p if n E { 1, 2, 5, 6], 2p if n = 3 and 3p when n = 4. What is the expected number of times the outcome is 4 when this die is rolled 954 times?