5. For each of the following, determine the constant k so that f(x) satisfies the conditionsof being a p.d.f. for a random variable X.(0) S(x)=k(a) f(x)=x+1x= 1,2,3,4(b) f(x)= k|x =1,2,3,4,...

We have given that the random variable X having pdf in discrete form. Here, need to find out the…

Answered: (a) f(x)= 5. For each of the following,…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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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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Let X be a continuous random variable described below: p(X) = x/4, for all x in the range 0 ≤ x ≤ 2 = x2/8, for all x in the range 2 < x ≤ k (a) What is the value of k?(b) What is E(X)? Note: Answers to both questions are irrational numbers.
Q1 Let X1 and X2 be independent exponential random variables with identical parameter A. Q1(i.) Find the distribution of Z = max(X1, X2). Q1 (ii.) Find the distribution of Y = min(X1, X2). Q1(iii.) Calculate E[Y]. Q1(iv.) Calculate E[Z]. Q1(v.) Using the relation Z = X1+X2 – Y, Calculate E[Z] and verify that it agrees with the calculation done in part (iv.)
The cumulative distribution function F(x) of a random variable X is given in the following table: 1 2 3 F(x) 0.5 b 1 a Let a and b are positive constants. If P(1 3) = 0.3. Then a and b equal to: a=0.1, b=0.3 None of these a=0.1, b=0.7 a=0.5, b=0.8
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Example 2.19 Let X be a random variable with possible values {x1, x2,...x) such that P(X = x) =!v i. Find E(X).
For each random variable defined here, describe the set of possible values for the variable, and state whether the variable is discrete. (d) X = the length of a randomly selected rattlesnake Describe the set of possible values for the variable. 0, 1, 2, 3, ... 1, 2, 3, ... [0, ∞) (0, ∞) State whether the variable is discrete. discrete not discrete (e) Z = the sales tax percentage for a randomly selected amazon.com purchase, where n = the total number of possible sales tax percentages for online purchases Describe the set of possible values for the variable. z1, z2, z3, ..., zn [0, zn] 1, 2, 3, ..., n [0, n] State whether the variable is discrete. discrete not discrete (f) Y = the pH of a randomly chosen soil sample Describe the set of possible values for the variable. 0, 1, 2, 3, ..., 14 [0, 14] 1, 2, 3, ..., 14 (0, 14] State whether the variable is discrete. discrete not discrete (g) X = the tension (psi) at which a randomly selected…
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Let pX(x) be the pmf of a random variable X. Find the cdf F(x) of X and sketch its graph along with that of pX(x) if pX(x)=1/3,x=−1,0,1, zero elsewhere

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(a) f(x)= 5. For each of the following, determine the constant k so that f (x) satisfies the conditions of being a p.d.f. for a random variable X. k (a) f(x)= x= 1,2,3,4 x+1 (b) f(x) =k: x =1,2,3,4,...