(h)(i)The geometric random variable counts the number of random events oc-curring in unit time.(j)True or FalseIf X and Y are independent, then 300(X) and 30s (Y) are dependent.8.If X~ Bin (6, 1/3) and Y~ Geom(1/4) are independent, then E(XY) =(k)The sum of two independent Poisson random variables with Poisson ratesof λ = 2 and μ = 5 respectively is a Poisson random variable with Poisson rateλ = 10.(1)If X is the number chosen randomly among the first ten positive integers,then E(X(11-X)) = 22.

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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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The distribution function for a random variable X is F (x) = {-e-", 20 x > 0 to x 2? e 2 e -5 -4 e
Random variable "Z" is distributed N(0,1). Find Pr(Z < 0.21). Enter your answer as a decimal rounded to three decimal places, e.g. 0.268.
1 (a) Discuss the two expressions -x;- )² and E(x;- )², both of which are used (n-1) i=1 to measure the spread of a set of observations x1, x2, . .., X. (b) A random sample of n observations is taken from a distribution; the sum of the observations is t, and the sum of the squares of the observations is 12. Explain how to estimate the mean and the variance of the distribution from which the random sample was taken. (c) Given the random sample described in part (b), write down expressions (based on 11 and t2) for estimates of the mean and variance of the mean of a further, independent, random sample of size m , from the original distribution. (d) Given that n = 25, 1, = 400 and t2 = 8800, construct a 99% confidence interval for the mean of the distribution, and use it to test whether or not this mean could be 20.
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triple of “heads” (h) and tails (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then R (hht)=1. Suppose that the random variable X is defined in terms of R as follows X=6R-2R^2-1. The values of X are given in the table below. A) Calculate the values of the probability distribution function of X, i.e. the function Px. First, fill in the first row with the values X. Then fill in the appropriate probability in the second row.
If a discrete random variable X has the following probability distribution: X -2, - 1, 0, 1, 2 P(X) 0.2, 0.3, 0.15, 0.2, 0.15 Use this to find the following: (a) The mean of X and E[X^2]. (b) The probability distribution for Y = 2X^2 + 2 (i.e, all values of Y and P(Y )). (c) Using part (b) (i.e, the probability distribution forY ), find E[Y ]. (d) Using part (a), verify your answer in part (c) for E[Y ]. **Note: Please do not just copy from Chegg!
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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
Use integration to solve, not probability methods, Calculus 2 problem. The speeds of vehicles on a highway with speed limit 90 km/h are normally distributed with mean 101 km/h and standard deviation 5 km/h. (Round your answers to two decimal places.) (a) What is the probability that a randomly chosen vehicle is traveling at a legal speed? % (b) If police are instructed to ticket motorists driving 115 km/h or more, what percentage of motorist are targeted? %
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