1. The discrete random variable X has a probability mass functionx = -2,-1x = 0,1x = 2otherwiseP(X=x)=-(0.1,B.0.2,(a) Find the value of B.(b) Construct the probability mass distribution of X.(c) Write the cumulative distribution function of X in functional form.F(x)=2. The discrete random variable X has a cumulative distribution function F(x) defined byx<1[0.8where k is a constant and x an integer.(a) Find the value of k if P(X=4)=(b) Write the probability mass function of X.[0,x+k8|1.1≤x≤3.x>33. Two chess players, Hello and Kitty, are playing each other in a series of games. The probabilitythat Hello wins the first game is 0.3. If Hello wins any game, the probability that she wins the nextis 0.4; otherwise, the probability is 0.2. For a series of three games, find the probability of X, thenumber of games that Hello wins.

The discrete random variable X has a probability mass function:Note: Hi there! Thanks for posting…

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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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A random variable x has a probability mass function defined by P(X=x) = r(x-1). if x= 2,3 r(8-x). if x=4,5,6 0. Otherwise Write out the probability mass function. What will be the expectation and variance of x. Find P (x greater or equal to 2 and less or equal to 5).
Please do these 3 Qs in excel or show steps, thank you.
Let X and Y have the following joint probability density function: fX,Y(x,y) = 1 / (x2 y2), for x>1, y>1 0, otherwise Let U = 5 X Y and V = 8 X. In all question parts below, give your answers to three decimal places (where appropriate). (a) The non-zero part of the joint probability density function of U and V is given by fU,V(u,v) = A vB uC for some constants A, B, C. Find the value of A.
Q1 Let probability distribution function of Xbe defined by х %3D 0,1, 2, 3. a P(x) = otherwise. Find the value of a. (а) (b) (c) (d) Find P(-1
[Q1] The probability distribution of the discrete random variable X is: f(X) = k23-* , for x = 4,5, 6, 7 (a) Find: • the value of the constant k. • The mean E (X). • The variance Var(X). (b) Sketch F(X).
Please answer this statistic question
Plzzz explain
If the joint probability distribution of X and Yis given by: (picture)Find P(X ≤ 2, Y = 1)Find P(X + Y = 4)Find P(X>Y )Find P(X > 2, Y ≤ 1)
1. Verify whether the following functions can be considered as probability mass functions: (i) P(x = x) = x² + 1 18 (iii) P(X= x) = -, x = 0, 1, 2, 3 (ii) P(X - x) - ²-2, -, x= 1, 2, 3 2x + 1 18 -, x = 0, 1, 2, 3 [Ans.: Yes) [Ans.: No] [Ans.: No]
The discrete random variables X and Y have the following joint probability function Y 0 1 2 1 1/20 2/20 3/20 X 2 2/20 1/20 4/20 3 3/20 1/20 3/20
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1. The discrete random variable X has a probability mass function (0.1, x=-2,-1 B. x=0,1 x = 2 otherwise P(X=x) = 0.2, [0, (a) Find the value of B. (b) Construct the probability mass distribution of X. (c) Write the cumulative distribution function of X in functional form.