1.- The random variable x represents the time interval between two consecutive arrivals at a storeand its probability density function is given byf(x) = { ke-x/2, x>0any other caseFor k any constant. Determine: a) the value of k, b) the cumulative distribution function, c) theprobability that 2

a) To determine the value of k for the probability density function (PDF) given bywe need to ensure…

Answered: 1.- The random variable x represents…

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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Find the value of k for the probability mass function 4 f(x) = k () , ) for x = 0,1,2. %3| 4 -
a) Let X be a continuous random variable with the following probability density function (2x3 f(x)={11 2 +5) , 0
Suppose that X is a continuous random variable with a probability density function is given by f(x)= 25 when x is between -2 and 2, and f(x)=0 otherwise. a.)Find E(X2), where X is raised to the power 2 b.) Find Var(2X+2)
7. Let X and Y denote two continuous random variables. Let f(x,y) denote the joint probability density function and fx(x) and fy (y) the marginal probability density functions for X and Y, respectively. Finally let Z = aX + bY, where a and b are non-zero real numbers. (e) Derive an expression for Cov(Z) as a function of Var (X), Var(Y) and Cov(X,Y). [You may use standard results relating to variance and covariance without proof, but these should be clearly stated.]
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Let X be a random variable with a uniform distribution on the interval (0,1). Given Y = e*, derive a) b) the probability distribution function of Y = ex. the probability density function of Y.
5. Let X be a random variable with a uniform distribution on the interval (0,1). Given Y = e, derive a) b) the probability distribution function of Y = e*. the probability density function of Y.
Suppose a college professor never finishes her lecture before the end of the class period, and always finishes within five minutes after the class period is supposed to end. Let X = time that elapses between the end of the class period and the actual end of the lecture. Suppose the pdf of X is: (image) Find the value of k that makes f(x) a legitimate probability density function, and use that value of k to find the probability that the lecture ends less than 3 minutes after the class period is supposed to end.
Let X be a random variable that follows the beta distribution. This random variable is continuous and is defined over the interval from 0 to 1. The probability density function is given by whereand are integers, whose values determine the shape of the probability density function. Because X varies between 0 and 1, we can think of X as the probability that some event (say) E occurs or the proportion of times an event occurs in some population. For example, E could denote the event that a critical part in a newly designed car will lead to a catastrophic failure in accidents at high speeds. The expected value (i.e., mean) of this random variable is []. That is, . The Excel commands for the beta random variable are =beta.dist(x,,,true,0,1) for the cumulative probability distribution, and =beta.dist(x,,,false,0,1) for the probability density function. (a) Now, think in Bayesian terms.…

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