Question 2 (20 points) Let X be a random variable that represents the sum of rolling...
Let X be a random variable corresponding to the sum of scores obtained from rolling two dice. Calculate the following probabilities: 1) p(X ≥ 5) 2) p(8≤ X ≤ 10) 3) p(X ≤ 2)
Let X1 be a random variable whose value is the result of rolling an 8- sided die, and X2 a random variable whose value is the result of rolling a 12-sided die. (1) Find E(X1 + X2). (2) Find E(X{ + Xž). (3) Find V(X1 + X2).
5. Let X be a discrete random variable. The following table shows its possible values r and the associated probabilities P(X -f(x) 013 (a) Verify that f(x) is a probability mass function (b) Calculate P(X < 1), P(X < 1), and P(X < 0.5 or X > 2). (c) Find the cumulative distribution function of X ompute the mean and the variance of
7 Let Xbe a random variable whose values are the number of dots that appear on-the uppermost face r die is rolled. The possible values of Xare 1,2,3,4,5, and 6 The mean of & is and the variance of of X is 3 Let Y be the random variable whose value is the difference (first minus second) between the number t face for the first and second rolls of a fair die that is rolled twice. What is mean ofXis...
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12. (15 points) Let X be a continuous random variable with cumulative distribution function 0. F(x) = Inc. <a a<x<b bcx 1. (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
Let X be an exponential random variable with parameter A > 0, and let Y be a discrete random variable that takes the values 1 and -1 according to the result of a toss of a fair coin Compute the CDF and the PDF of Z = XY
Let X be an exponential random variable with parameter A > 0, and let Y be a discrete random variable that takes the values 1 and -1 according to the result of...
7. (3 points) Given a fair 6-sided die. Each time the die is rolled, the probabilities of rolling any of the numbers from 1 to 6 are all equal. 1) If it is rolled once and let A be the event of rolling a number larger than 3 and B be the event of rolling an odd number. What is P(AV B)? 2) If it is rolled three times, what is the probability that the same number shows up in...
3. Compute the variance of X when X is the result of rolling a fair die. 4. Let X be a random variable with density function 1 0<z<1 0 otherwise f(x)= What is the variance of X.
X is a Random variable representing the outcome of rolling a 6-sided die. Before the die is rolled, you are given two options: (a) You get 1/E(X) in Points right away. (b) You wait until the die is rolled, then get 1/X in Points. Which option is better in getting Points?
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Consider the probability experiment of rolling two 6-sided dice, and the associated random variable X = sum of the two dice. () (3 points) See the OpenLab poet which includes the sample space for this experiment, and gives part of the proba bility distribution of Complete the exercise by filling in this table to get the full probability distribution of X Sum of the two dice, Outcomes in the event (X=;} Probability PCX-23) 1/36 = 0.0278 3 {(1,2),...