1. Suppose that that joint probability mass function of and is given in the following table.
y | |||
0 | 1 | ||
0 | 0.16 | 0.14 | |
1 | ? | 0.17 | |
2 | 0.11 | 0.11 |
Find .
Hint: Find first.
2. Suppose that that joint probability mass function of and is given in the following table.
0 | 1 | ||
0 | 0.06 | 0.08 | |
1 | ? | 0.09 | |
2 | 0.14 | 0.05 |
Find the expected
value of .
1. Suppose that that joint probability mass function of and is given in the following table....
The following table presents the joint probability mass function pmf of variables X and Y 0 2 0.14 0.06 0.21 2 0.09 0.35 0.15 (a) Compute the probability that P(X +Y 3 2) (b) Compute the expected value of the function (X, Y)3 (c) Compute the marginal probability distributions of X and )Y (d) Compute the variances of X and Y (e) Compute the covariance and correlation of X and Y. (f) Are X and Y statistically independent? Clearly prove...
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...
n a certain community, levels of air pollution may exceed federal standards for ozone or for particulate matter on some days. For a particular summer season, let X be the number of days on which the ozone standard is exceeded and let Y be the number of days on which the particulate matter standard is exceeded. Assume that the joint probability mass function of X and Y is given in the following table: y x 0 1 2 0 0.10...
ques In a certain community, levels of air pollution may exceed federal standards for ozone or for particulate matter on some days. For a particular summer season, let X be the number of days on which the ozone standard is exceeded and let Y be the number of days on which the particulate matter standard is exceeded. Assume that the joint probability mass function of X and Y is given in the following table: Find the marginal probability mass function...
Suppose that the following table is the joint probability distribution of two random variables X and Y: х -2 0 2 3 0.27 0.08 0.16 0.2 0.1 0.04 0.1 0.05 a. Find the marginal PDF of X when x=-2, 0, 2, and 3. b. Find the marginal PDF of Y when y=2 and 5. . Find the conditional PDF of x=-2 and 3 given that y=2 has occurred. . Find the conditional PDF of y=2 and 5 given that x=3...
Given here is the joint probability function associated with data obtained in a study of the auto-mobile accident in which a child (under age 5 years) was in the car and at least one fatality occurred. Especially, the study focused on whether or not the child survived and what type of seatbelt (if any) he or she used, yı = 0, if the child survived, yi = 1 if not and y2 = 0, if no belt used y2 =...
2. The number of cars passing through each lane of a toll booth per minute is represented by a random variable, C, and the number of trucks passing through it is represented by another random variable, T. During the morning peak hour, the joint probability mass function of C and T is given by the following table 0 0.05 0.08 0.08 1 0.05 0.09 0.11 0.08 0.22 0.11 0.06 0.05 0.02 Find the marginal probability mass function of T, pr(t)...
Exercise 10.1. The joint probability mass function of the random variables (X, Y) is given by the following table: 0 12 01 21 醋慹!) 죄 9 (a) Find the conditional probability mass function of X given Y -y. (b) Find the conditional expectation Elxy-y] for each of y = 0, 1, 2.
1. actuarial LTAM question You are given: (1) Hv = 0.02 for 0 sts 10. (i) 8 = 0.08 (iii) Y is the present value random variable for a 10-year temporary continuous life annuity due on (x). Find the probability that Y is less than 0.75E(Y). Select one: a. 0.05 b. 0.14 c. 0.08 d. 0.11 e. 0.17
The discrete random variables ? and ? have joint probability function ?, where ? is given by the following table: X 1 2 3 4 1 0.1 0.2 0.1 0.05 Y 2 0.05 0 0.1 0.1 3 0 0.2 0.05 0.05 a) Determine ?(1 < ? ≤ 3, 1 ≤ ? ≤ 2). [4 marks] b) Calculate ?(?^2 ?). [4 marks] c) Find the marginal probability functions ? and ℎ of ? and ? respectively. [4 marks] d) Are ?...