Let X denote a random variable that takes on any of the values -1, 0, 1 with respective probabilities P(X = −1) = 0.2,P(X = 0) = 0.5,P(X = 1) = 0.3. Compute E(X2). (a) 0.2 (b) 0.3 (c) 0.4 (d) 0.5 (e) None of the above

Let X denote a random variable that takes on any of the values -1, 0, 1 with respective probabilities P(X = −1) = 0.2,P(X = 0) = 0.5,P(X = 1) = 0.3. Compute E(X2). (a) 0.2 (b) 0.3 (c) 0.4 (d) 0.5 (e) None of the above

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...

See similar textbooks

Related questions

Q: f x is a binomial random variable, compute p(x) for each of the following cases: (a) n=3,x=1,p=0.5…

A: a) n=3,x=1,p=0.5 P(X=1)=3C1 * 0.51*0.53-1 =0.375

Q: (a) P(x ≤ 4), n = 6, p = 0.9 P(x) = (b) P(x > 5), n = 9, p = 0.6 I P(x) = (c) P(x < 3), n = 4, p =…

Q: 9) You are given the following data regarding the probabilities of two events E and F: P(EUF) = 0.8,…

A: For any two events A and B, union of A and B, is the occurrence of either A or B or both. In other…

Q: Example 2.15. Let X be a random variable with the following pdf: + 1. Find its CDF. 2. Evaluate the…

Q: Let X be a Poisson random variable with A - :3 and Y be a Poisson random variable with X = 4. Assume…

Q: Find E (X) and E(X²) and using these values evaluate E[(2X + 1)²]

Q: 1-4x 10) If a random variable assumes 4 values with probability 1+3x 1-x 1+2x and ¹-4 4 4 4 the…

A: Here for given probability check whether using value of x total probability is equal to 1 and all…

Q: (1) E(E(X)) = E(X) (2) E(X – E(X)) = 0 (3) Var(X) = E(X²) – [E(X)]² (4) Given constants a and b,…

A: Discrete random variable is defined as a variable which can take only specific values. For example…

Q: Let X1 and X2 be independent random variables with respective binomial distributions b(3,1/2) and…

A: The provided information is as follows:The and are two independent variables.The follows binomial…

Q: If x is a binomial random variable, compute P(x) for each of the following cases: (a) P(x ≤ 4), n =…

A: Considering the random variable x is a Binomial random variable, i.e., the variable essentially…

Q: 7. A discrete random variable X taking non-negative integer values has probability gen- erating…

Q: Suppose a random variable X has expected value E[X] quantities. (a) E[X-1] (b) E[X²] (c) E[(X− 1)²]…

A: Note:- Since you have posted a question with multiple subparts we will provide solutions only to the…

Q: 1. Suppose X~ N(₁,02), i = 1,..., n are independent random variable State the distribution of each…

A: Note: According to Bartleby guidelines expert solve only one question and maximum three subpart of…

Question

Let X denote a random variable that takes on any of the values -1, 0, 1 with respective probabilities P(X = −1) = 0.2,P(X = 0) = 0.5,P(X = 1) = 0.3. Compute E(X2).
(a) 0.2
(b) 0.3
(c) 0.4
(d) 0.5
(e) None of the above

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given

VIEW

Step 2: Compute E(X2).

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

17
A particle executes an unrestricted simple random walk on the line with p=0.7 and q=0.3. Its position at time n is represented by the random variable Xn, n = 0, 1,...; Xo = 0. (a) Calculate the values of the following probabilities. (i) P(X5 = -2) (ii) P(X6 = 2) (b) Calculate the probability that the particle returns to its starting point for the first time after 8 steps. (c) After the particle has been moving for some time, it is observed to be located at the point +3. (i) Calculate the probability that the particle will ever return to the origin from the point +3. (ii) Calculate the probability that starting from the point +3, the particle will visit the point +8 without first visiting the origin.
B5. Let X₁, X₂, ..., Xn be IID random variable with common expectation µ and common variance o², and let X = (X₁ + + X₂)/n be the mean of these random variables. We will be considering the random variable S² given by (a) By writing or otherwise, show that S² (b) Hence or otherwise, show that n S² = (x₁ - x)². = Ĺ(X₂ i=1 X₁ X = (X₁-μ) - (x-μ) = Σ(X; -μ)² - n(X - μ)². i=1 ES² = (n-1)0². You may use facts about X from the notes provided you state them clearly. (You may find it helpful to recognise some expectations as definitional formulas for variances, where appropriate.) (c) At the beginning of this module, we defined the sample variance of the values x₁, x2,...,xn to be S = 1 n-1 n i=1 ((x₁ - x)². Explain one reason why we might consider it appropriate to use 1/(n-1) as the factor at the beginning of this expression, rather than simply 1/n. B6. (New) Roughly how many times should I toss a coin for there to be a 95% chance that between 49% and 510/ of my nain toon land Honda?
7. A discrete random variable X taking non-negative integer values has probability gen- erating function: 1 rx(t) = (2- t)2 (a) Calculate P(X = 2).
Q2/(a) Let Xbe a random variable with p.d.f. 1
(1) Let X be a random variable with p.d.f. ke 3 0
Answer no. 1 only
2. The discrete random variable X has the probability function kx, P(X = x) = }k(x – 2), 0, x = 2,4,6 x = 8 otherwise Where k is a constant. (a) Show that k %3D 18 (b) Find the exact value of F(5).
Let X = b(n, and E(3x) = E(3-5x) find n.