Probability: Joint Probability Mass Function, Covariance and Variance

Let X and Y have joint probability mass function Pr{X = i, Y = j}= c(i + 1)(j + 2) for
i >= 0, j >= 0, and i + j < 4. Determine
a) the marginal probability mass function of X
b) the probability mass function of Y
c) the conditional probability mass function of X given Y = 0
d) the probability mass function of Z = X + Y
e) the conditional probability mass function of Z given X = 0
f) the mean of X
g) the expected value of Y
h) the mean of Z
i) the variance of X
j) the variance of Y
k) the variance of Z
l) the mean of XY
m) the covariance of X and Y
n) the mean of X conditioned on Y=0

Solution Summary

Fourteen statistical quantities are calculatd from a joint probability mass function. The solution is detailed and well presented.

Absolutely lost on how to determine what is being asked in below problem.
Consider the following jointprobability distribution for uncertain quantities X and Y:
P(X=-2 and Y = 2) = 0.2
P(X=-1 and Y = 1 = 0.2
P(X= 0 and Y = 0 = 0.2
P(X= 1 and Y = 1 = 0.2
P(X= 2 and Y = 2) = 0.2
1. Need to calculate the covariance a

2.) Suppose X has probabilitymass function Pr{X = k} = c(k + 2) for k = -1, 0, 1, 2 . Find c, and compute the mean, variance, and standard deviation of X.
Let Y = 3X + 5. Compute the mean, varianceand standard deviation of Y

1. There are five computers in an office. The probability of failure of a computer is 0.3. What is the probability that (a) there are 3 computers working, and (b) at least three computers working?
2. A computer service company is interested in the number of computers that fail. There are hundreds of computers in use in their

A fair coin is tossed four times and X is number of heads on first three tosses and Y on last three. What is the jointprobabilitymass function of x and y? What is the marginal pmf? Are X and Y independent?

Problem 5. An airline tracks data on its flight arrivals. Over the past six months, 65 flights on one route arrived early, 273 arrived on time, 218 were late, and 44 were cancelled
? a. What is the probability that a flight is early? On time? Late? Cancelled?
? b. Are these outcomes mutually exclusive?
? c. What is the pr

Determine the value of c that makes the function f(x,y) = c(x+y) a jointprobability density function over the range:
x greater than 0 and less than 3 and x less than y less than x+2
a) P(X<1, Y<2)
b) P(11)
d) P(X<2, Y<2)
e) E(X)
f) V(X)
g) Marginal probability distribution of X
h) Conditional probabilit

A frequency distribution is shown below. Complete parts (a) through (e).
The number of dogs per household in a small town
Dogs 0 1 2 3 4 5
Households 1157 417 168 45 26 16
a) Use the frequency distribution to construct a probability distribution.
X