a) In each of the following pmfs, find the value of C. i) p(x) Cx, x...
5. Let X be a discrete random variable with the following PMF: for x = 0 Px(x)- for 1 for x = 2 0 otherwise a) Find Rx, the range of the random variable X. b) Find P(X21.5). c) Find P(0<X<2). d) Find P(X-0IX<2)
Consider a random variable X with PMF Px(X) ={ cx x = 1,2,...,5 I found the value of c to be 1/15 1. find the complete expression for the CDF of X. 2. Find E[X], the expected value of X.
I just need the second problem done. Problem #2 refers to the
problem #1.
Problem # 1. Let discrete random variables X and Y have joint PMF cy 2,0,2 y=1,0, 1 otherwise = Px.y (x, y) 0 Find: a) Constant c X], P[Y <X], P[X < 1 b) P[Y 2. Let X and Y be the same as in Problem # 1. Find: Problem a) Marginal PMFs Px() and Py(y) b) Expected values E[X] and E[Y] c) Standard deviations ox...
The random variable X has CDF 0 <-1, Ex(x) = 0.2 -1 < 0, 0.7 0 x<1, 1 21. (a) Draw a graph of the CDF (b) Write Px(), the PMF of X. Be sure to write the value of Px(a) for all r from-oo to oo. Given the random variable X in problem ii), let V g X)X. (a) Find P(v). (b) Find Fy(v). (c) Find EIV]
Which of the following is/are required for the probability distribution of a discrete random variable X with probabilities P(X= x), to be valid? I. PX x) is between 0 and 1 for all values of x. 2aPXx) ii. all x i, all x2 0 Il and Ill only Il only I and Il only I, II, and III only
Proposition 6.10 Independent Discrete Random Variables: Bivariate Case Let X andY be two discrete random variables defined on the same sample space. Then X and Y are independent if and only if pxy(x,y) = px(x)py(y), for all x , y ER. (6.19) In words, two discrete random variables are independent if and only if their joint equals the product of their marginal PMFs. Proposition 6.11 Independence and Conditional Distributions Discrete random variables X and Y are independent if and only...
. Assignment of probability p, to each value of the Continuous Random Variable x. B. Assignment of frequency f, to each value of the Discrete Random Variable x. C. Assignment of probability p, to each value of the Discrete Random Variable x. D. Assignment of frequency f, to each value of the Continuous Random Variable x. Given the discrete probability distribution in the table below, answer questions 12-15 23 4 Po)10.12a a-0.11 0.28 12. Calculate a A. 0.46 B. 0.33...
2. The joint probabilities P(X = a, Y = b) of two discrete random variables X and Y are given in the following table: 4 1 2 1 / 2 3 16/1363/1362/136 13/136 5/136 | 10/136 11/136 | 8/136 9/136 6/136 | 7/136 | 12/136 4/136 15/136 14/136 1/136 3 4 d. Determine the marginal PMF of X and Y e. Determine the following probabilities of X and Y from the table: a. P (X=1, Y=2) b. P (X=3) c....
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...
P(x=a) 1 Note that for a discrete random variable, 0 Therefore P(xS a)? P(x<a) A.= C. 7 D. 2