. Suppose the discrete random variable X represents the number of a-particles discharged in a fixed...
Looking for help on question f and beyond 1. Suppose the discrete random variables X and Y have joint pmf (a) Find P(X < 1,Y 2 2) (b) Find P(Y-2) (c) Find P(x -Y) d) Find the marginal pmf of X, fx(x). Be sure to state the support (e) Find E(X) (f) Find the conditional pmf of Y given X- r, fy|x-»(b). Be sure to state the support (and the values a that can be conditioned on) (g) Find the...
Suppose that X is a discrete random variable with pmf, p(x), arn x1 and x2 be numerical values in the range of X. dCDEFGT-Let- What should be in the blank space? F(0) Fx1)
4- Let Y = X, where X is a discrete uniform integer random variable in the range [-4,4). a) What is the PMF of the variable X? b) What is the PMF of the variable Y? c) Draw the PMF of the variables X, and Y. d) Draw the CDF of the variables X, and Y. e) What is the expected value of the random variables X and Y? f) What is the variance of the random variables X and...
Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of people with blood type Upper A in a random sample of 17 peoplepeople with blood type A in a random sample of 17 people. (b) The amount of rain in City Upper B during Aprilamount of rain in City B during April. (a) Is the number of people with blood type Upper A in a random...
Let X be a discrete random variable, and let Y X (a) Assume that the PMF of X is Ka2 0 if x- -3, -2,-1,0,1,2,3 otherwise, where K is a suitable constant. Determine the value of K. (b) For the PMF of X given in part (a) calculate the PMF of Y (c) Give a general formula for the PMF of Y in terms of the PMF of X
The discrete random variable X is the number of passengers waiting at a bus stop. The table below shows the probability distribution for X. What is the expected value E(X) for this distribution? X 0 1 2 3 Total P(X) .40 .30 .20 .10 1.00 1.1 1.0 1.7 1.9
Suppose that X is a discrete random variable which represents the number of bicycles per household in a town of 1000 households. Consider the following probability distribution below. 1 2 4 0.125 РСХ) 0.256 0.108 0.083 k 21. Determine the value of k and interpret this result. 22. Construct a graph of the probability distribution with appropriate labeling. 23. Find and interpret P(1XS3) 24. Calculate and interpret ux. 25. Calculate and interpret ax.
1 3 4 9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: Yl-1 0 1 0.1 0.1 0.1 0 0.2 0.1 0.2 0.1 0.1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. (11) b. Let W = X - Y. Compute E(W) and V(W). [4] 10. Let X be a continuous random variable with probability density function h(x) ce* r >...
Suppose 2 dice are rolled, and suppose the discrete variable x counts the number of 3’s thats how up. Plot the probability distribution for x using a bar graph. What is the expected value for the random variable x? What is the variance for the random variable x?
ciule jolh! PMF and the marginal PMFs? 6.14 Let X and Y be discrete random variables. Show that the function p: R2 R defined by p(r, y) px(x)pr(y) is a joint PMF by verifying that it satisfies properties (a)-(c) of Proposition 6.1 on page 262. Hint: A subset of a countable set is countable CHAPTER SIX Joindy Discrete Random Variables 6.2 Joint and marginal PMFs of the discrete random variables x numher of bedrooms and momber of bwthrooms of a...