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ke A* b.) A random variable X takes all positive integral values with P(X = x) 3D x! x 1,2,3,.. and k and A are positive constants. Find k in terms of 2. Hence, find the mean value of X.

ke A* b.) A random variable X takes all positive integral values with P(X = x) 3D x! x 1,2,3,.. and k and A are positive constants. Find k in terms of 2. Hence, find the mean value of X.

A First Course in Probability (10th Edition)
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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a.) A continuous random variable X has probability density function f given by f(x) = sk(1 - ax) for 0SxS2 0 elsewhere %3D where k and a are positive constants. Show that a . Express k in terms of a. Given that the mean of the distribution is find the value of k. b.) A random variable X takes all positive integral values with P(X = x) = x! ke d -,x= 1,2,3,.. and k and A are positive constants. Find k in terms of A. Hence, find the mean value of X. c.) Given that the probability that a child is left-handed is 20%, calculate, to 3 significant figures, the probability that, in a random sample of 5 children, at least 2 are left-handed. Use the normal approximation, to estimate, to 2 significant figures, the probability that in a school with 1600 pupils, between 330 and 350 are left-handed.
Transcribed Image Text:a.) A continuous random variable X has probability density function f given by f(x) = sk(1 - ax) for 0SxS2 0 elsewhere %3D where k and a are positive constants. Show that a . Express k in terms of a. Given that the mean of the distribution is find the value of k. b.) A random variable X takes all positive integral values with P(X = x) = x! ke d -,x= 1,2,3,.. and k and A are positive constants. Find k in terms of A. Hence, find the mean value of X. c.) Given that the probability that a child is left-handed is 20%, calculate, to 3 significant figures, the probability that, in a random sample of 5 children, at least 2 are left-handed. Use the normal approximation, to estimate, to 2 significant figures, the probability that in a school with 1600 pupils, between 330 and 350 are left-handed.
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