Expected values and Binomial distribution10. A cubical die is biased. The numbers one to five are equally likely to land face up, but six is twiceas likely to land face up as each of the other numbers. If X is the score shown on the uppermostface, calculate the expected value of X. State your answer in mixed fraction

A cubical die is biased. The numbers one to five are equally likely to land face up, but six is…

Answered: calculate the expected value of X.S

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...

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Calculate the mean value (expected value) of the following discrete variable x: x-0, 1, 2, 3, 4, 5, 6 %3D p(x) 3D 0.2, 0.2, , 0.05 0.15,0.15, 0.15, 0.1
Answer number 4
1 A random variable X has a mean of 10 and variance of 9 and is of unknown distribution. Find p (5 < X < 15).
Prove the property
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3 500 0≤x≤ys 10 1. Find the expected value of Y. f(x, y) =
The geometric distribution gives the probability that the first success occurs at the xth trial with success probability p. f(x)=(1-p)x-1p, x=1,2,3,... Show that E(X)=1/p
Losses come from a mixture of an exponential distribution with mean 100 with probability p and an exponential distribution with mean 10,000 with probability 1– p. Losses of 100 and 2000 are observed. Determine the likelihood function of p. -0.01 pe (1– p)e“ pe 20 (1– p)e0² -0.2 (A) 100 10,000 100 10,000 pe (1– p)e“ -0.01 (B) pe (1– p)e02' 100 10,000 100 10,000 pe, (1- p)e0. 20 (1– p)eº -0.01 pe 100 -0.2 (C) pe 10,000 100 10,000 pe, (1- p)e 00i -0.01 (D) -20 ре (1– p)e02 100 10,000 100 10,000 e 0.01 +(1– p) e -20 (E) р. 100 10,000 100 10,000
4. An insurance company sells an automobile policy with a deductible of one unit. Let X be the amount of the loss having pmf 0.9 f(x) = x = 0 x = 1,2,3,4,5,6 where c is a constant. a) Find c. b) Find the expected value of the amount the insurance company must pay.
Five males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the X-linked genetic disorder. Detemine whether a probability distribution is given. If a probability distribution is given, find its mean and standard P(x) 0.034 0.157 1 2 deviation. If a probability distribution is not given, identify the requirements 0.309 3 0.309 that are not satisfied. 4 0.157 5 0.034 Does the table show a probability distribution? Select all that apply. O A. Yes, the table shows a probability distribution. B. No, the random variable x's number values are not associated with probabilities. C. No, not every probability is between 0 and 1 inclusive. O D. No, the random variable x is categorical instead of numerical. O E. No, the sum of all the probabilities is not equal to 1. Find the mean of the random variable x. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. µ= O B.…
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0.10.20.40.5

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