The formula for E(X) =
XP(X)
V(X) = E(X2) - E2(X)
=. X2P(X)
- E2(X)
Now we construct the following table for calculation
X | P(X) | XP(X) | X2P(X) |
0 | 0.3 | 0 | 0 |
2 | 0.35 | 0.70 | 1.4 |
4 | 0.35 | 1.4 | 5.6 |
Total | 2.1 | 7 |
Therefore by the formula we have
E(X) =XP(X)
= 2.1
V(X) = 7 - (2.1)2 = 7 - 4.41 = 2.59
4. (10 points) X are discrete random variables. The following table summarizes the probability mass function...
The table below gives the joint probability mass function of a pair of discrete random variables X and Y. Pxr(x,y) 12 3 P) 10.30 0.05 0.15 2 0.10 0.05 0.35 px(x) Complete the marginal distributions in the table above. . Are X and Y independent? Yes Check
1. Suppose X and Y are discrete random variables with joint probability mass function fxy defined by the following table: 3 y fxy(x, y) 01 3/20 02 10 7/80 3/80 1/5 1/16 3/20 3/16 1/8 2 3 2 3 a Find the marginal probability mass function for X. b Find the marginal probability mass function for Y. c Find E(X), EY],V (X), and V (Y). d Find the covariance between X and Y. e Find the correlation between X and...
20. (8 points) Suppose X, Y, and Z are discrete random variables with joint probability mass function P(x, y, z) given below. Be sure to full justify your answers and show ALL work. P(0,0,0) = 2,3 P(0,0,1) 33 P(0,1,0) = P(1,0,0) = 32 P(1,0,1) = P(1,1,0) = 32 a. Find the marginal probability mass function for 2, pz(2). b. What is E[X | Y = 0]? P(0,1,1) = 4 P(1,1, 1) = 32
Question 4: Let X and Y be two discrete random variables with the following joint probability distribution (mass) function Pxy(x, y): a) Complete the following probability table: Y 2 f(x)=P(X=x) 1 3 4 0 0 0.08 0.06 0.05 0.02 0.07 0.08 0.06 0.12 0.05 0.03 0.06 0.05 0.04 0.03 0.01 0.02 0.03 0.04 2 3 foy)=P(Y=y) 0.03 b) What is P(X s 2 and YS 3)? c) Find the marginal probability distribution (mass) function of X; [f(x)]. d) Find the...
0 Consider the discrete random variables X and Y with the following joint probability mass function: . -1 1/8 0 1/4 0 1 1/4 1/8 -1 1 1/8 1/8 What is P(X = 1 Y = 0)? Are X and Y independent? 0 A. 0; independent B. 1/2; independent C. 1/2; dependent D. 1/8: dependent E. none of the preceding
Problem 5 Define X and Y to be two discrete random variables whose joint probability mass function is given as follows: e-127m5n-m P(X = m, Y = n) = m!(n - m)! for m <n, m> 0 and n > 0, while P(X = m, Y = n) = 0 for other values of m, n 1. Calculate the probability that 1 < X <3 and 0 <Y < 2. 2. Calculate the marginal probability mass functions for the random...
Consider the discrete random variables X and Y with the
following joint probability
mass function:
Given that X is not negative, what is the probability that Y is
also not negative?
A. 0.5 B. 0.8 C. 0.4 D. 0.25 E. none of the preceding
T -1 0 0 Y 0 -1 1 0 1 -1 fxy(x,y) 1/8 1/4 1/4 1/8 1/8 1/8 1 다.
Consider the discrete random variables X and Y with the following joint probability mass function: 2 y fxy(x,y) -1 0 1/8 0 -1 1/4 0 1/4 0 1/8 -1 1/8 1 -1 1/8 What is P(X = 1 Y = 0)? Are X and Y independent? 1 1 1 A. 0; independent B. 1/2; independent C. 1/2; dependent D. 1/8; dependent E. none of the preceding 3. Multiple Choice Question Suppose that the number of bad cheques received by a...
using excel answer the problem below
Let X be a discrete random variable having following probability distribution. x 2 4 6 8 P(x) 0.2 0.35 0.3 0.15 Complete the following table and compute mean and variance for X x P(x) x· P(x) x2. P(x) 2 0.2 4 0.35 6 0.3 8 0.15 Total 1 Expected value E(X) = u = Variance Var = o2 =
Question 1. A Discrete Distribution - PME Verify that p(x) is a probability mass function (pmf) and calculate the following for a random variable X with this pmf 1.25 1.5 | 1.7522.45 p(x) 0.25 0.35 0.1 0.150.15 (a) P(X S 2) (b) P(X 1.65) (c) P(X = 1.5) (d) P(X<1.3 or X 221) e) The mean (f) The variance. (g) Sketch the cumulative distribution function (edf). Note that it exhibits jumps and is a right continuous function.