Answered: Consider a random variable with the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Find E(X), Var(X), and the standard deviation of X, where X is the random variable whose probability table is given in the table below. Outcome 1 2 3 1 1 Probability 5 5 What is the expected value of the random variable X associated with the probability table given in the problem statement? E(X) = 12 5 (Type an integer or a simplified fraction.) What is the variance of the random variable X? Var(X) = (Type an integer or a simplified fraction.) 35 ■ . = C (-) Moro
The random variable x, representing the number of chocolate bar has the following probability distribution. Compute the mean x 0. 1. 2. 3. 4 P(x) 1/10 3/10 3/10 2/10 1/10
Consider the following discrete probability distribution: x P (x) 5 0.1 10 0.15 15 0.25 20 0.5 Calculate the expected value of the random variable. Calculate the variance of x Calculate the standard deviation of x.
19
The probability distribution of the number of students absent on Mondays, is as follows: X O 1 2 3 4567 f(x) 0.02 0.03 0.26 0.34 0.22 0.08 0.04 0.01 (a) What is the probability that more than 3 students are absent. (b) Compute the expected value of the random variable X. Interpret this expected value. (c) Compute the variance and standard deviation of the random variable X. (d) Compute the expected value and variance of Y : (e) Compute the covariance Cov(X, Y) = 7X+ 3. (f) What is the value of the ratio Cov(X,Y)/Var(X) ? (g) What is the value of Cov(X, Y)/Var(X) for Y = ß0 + ß₁X ? (For this exrcise, you can use excel. No need to show all calculations, just specify the formulas and present the final values.) (a) (b) (c) (d) (e) (f) (g)
A random variable X has the following distribution: X P(X=x) -1 .3 0 1 .5 2 Let Y=X². Find the expected value of random variable Y. 0.38 0.6 5 4 O-1
Consider the table below gives the probabilities of the distribution of random variable X. Value of X P(X=x) (denoted by x) f(x) 0 1 2 3 4 567 00 8 0.14 b C 0.10 0.13 0.13 d 0.02 0.01 In reference to the table, suppose that b = f(1) =0.2 and c = f(2)= 0.06. What is the probability P(X ≥ 4) equal to?
The mean incubation time of fertilized eggs is 21 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 1 day (a) Determine the 20th percentile for incubation times. (b) Determine the incubation times that make up the middle 95% of fertilized eggs. (a) The 20th percentile for incubation times is days. (Round to the nearest whole number as needed) (b) The incubation times that make up the middle 95% of fertilized eggs areto days. (Round to the nearest whole number as needed. Use ascending order)
Answer the second two questions
The annual premium for a $20,000 insurance policy against the theft of a painting is $350. If the (empirical) probability that the painting will be stolen during the year is 0.02, what is your expected return from the insurance company if you take out this insurance? Let X be the random variable for the amount of money received from the insurance company in the given year. E(X)= dollars
Compute the expected value for X. X 1 2 0 0.10 0.12 Y 1 0.05 0.10 2 0.02 0.16 3 0.06 0.11 0.28
Calculate the mean value (expected value) of the following discrete variable x: x-0, 1, 2, 3, 4, 5, 6 %3D p(x) 3D 0.2, 0.2, , 0.05 0.15,0.15, 0.15, 0.1

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Consider a random variable with the following probability distribution: X P(X) 0 0.25 1 0.5 2 0.25 What is the expected value (mean) of X?