E ze 3. A random variable X has the following probability function.1.46.7Values of Xp(x)0.K2K2K3KK?2K?7K? + K(1) Find K.(2) Evaluate P(X < 6), P(X > 6) and P(0 X < 5).(3) If P(X £ K) >find the minimum value of K and v paisimil ad o2(4) Determine the distribution function of X.0ng hotnaio hsllas Peldmotudittaib noteaio9 auglisate baa

Answered: E ze 3. A random variable X has the…

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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Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(X)=0 Var(X) = 39 Var(Y) = 19 Var(Z) =24 E(Y) =-4 E(Z)=6 Compute the values of the expressions below. E(1+5z) = -Y-4Z E 2 Var(4–3Y) = I E(sz²) = I
1. A probability distribution is made by a school to record the number of phone calls from parents they receive per day. It is illustrated below. X: P(X) P(X) X-H (X – µ)? P(X)·(X – µ)? 5 0.15 6 0.15 0.9 -1 1 0.15 7 0.4 0.15 1.2 1 0.15 9 0.15 a) Construct a histogram that would best represent the probability distribution. b) Compute the expected number of phone calls from parents received per day. c) Complete the table above and find the variance and standard deviation. d) What is the probability of receiving more than 6 phone calls? e) What is the probability of receiving at most 7 phone calls?
Exercise 3. Let X be a random variable with mean µ and variance o². For a € R, consider the expectation E((X − a)²). a) Write E((X - a)²) in terms of a, μ and σ². b) For which value a is E((X − a)²) minimal? c) For the value a from part (b), what is E((X − a)²)?
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(X)=5 Var(X) = 44 Var(Y)=23 Var(Z) = 32 E (Y)=-2 E(Z)=-4 %3D %3D Compute the values of the expressions below. E(-5+5Y)= | 3Y+5X E -3 Var(5X-5) = I E-2
A random variable X has a following probability function, X 0 1 3 4 5 6 P(X) 0k 2k 2k | 3k k 2k 7k2 + k Find the value of, (i) k (ii) P(X < 6).
Suppose that X, Y, and Z are jointly distributed random variables, that is, they are defined on the same sample space. Suppose that we also have the following. E(X)=-1 E(Y) = 4 E (Z)=0 Var(X)=20 Var(Y) = 27 Var (Z) = 38 Compute the values of the expressions below. E (5Z-2) = 0 2Z+X -5 Var(2X-3) = 0 E = E (32²) = 0 Explanation Check X O hp Ⓒ2022 McGraw Hill LLC. All Rights Reserved. Term
A discrete random variable X has the cumulative distribution function given by the following diagram. Find P(X<= 2) and P(X=2) * {. x2 if x = 1, 2, 3 9 F(x) = otherwise. 3/9 and 2/9 7/9 and 3/9 5/9 and 2/9 O 4/9 and 3/9
Probabilities
A- Let x be a discrete random variable with probability distribution function f(x)=k( x2 +20) and x= −1,1,2,3. Find the value of k. Find the Variance of X. B- Let x denote a discrete random variable which can take the values −2,0, and 5. Given that the expectation of X is 8/100 and P(X=−2)=8/20 , find P(X=5).
3. Determine the value c so that each of the following functions can serve as probability distributions of the discrete random variable X: a. f(x) = c(x² +4) for x = 0,1, 2, 3; 3 b. f(x)%3Dс for x= 0,1, 2 3-x
Random Variables X and Y are independent. They have probabilities given here: (attached) It is understood that ‘m’ has a numeruc value. Let T be a random variable equal to the sum of X and Y. Find P(T=4).
Example 2.14. Show the CDF of the random variable X with the following pdf: Sx(2) = lwa(x) Example 2.15. Let X be a random variable with the following pdf: 1. Find its CDF. 2. Evaluate the following probabilities using its CDF and/or pdf. a) P(} 1) c) P(X > }|X < 1)

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