Consider two events X and Y that have marginal probabilities of 0.68 and 0.57 respectively. Their joint probability is 0.35. Calculate the probability that event X occurs if Y has occurred. (3 decimal places)
Conditional probability is the probability of intersection of X and Y divided by the marginal probability of an event which has already occurred.
Pr(X/Y) = Pr(X,Y)/Pr(Y) =0.35/ 0.57= 0.614
Consider two events X and Y that have marginal probabilities of 0.68 and 0.57 respectively. Their...
7. Let X, and X, be indicators of independent events with probabilities 1/2 and 1/3. respectively. a) Display the joint distribution table of X2 + Xs and X - Xs. b) Calculate E(X3 - X) C) Are X and Xs uncorrelated? Prove your answer.
O PROBABILITY Probabilities involving two mutually exclusive events Events A and B are mutually exclusive. Suppose event A occurs with probability 0.03 and event B occurs with probability 0.02. a. Compute the probability that A does not occur or B does not occur (or both). b. Compute the probability that neither the event A nor the event B occurs. (If necessary, consult a list of formulas.) 6 2
Consider the following probabilities: P(AC) 0.57, PB = 0.36, and P(A n B) 0.03 a. Find P(A | BC). (Do not round intermediate calculations. Round your answer to 2 decimal places.) P(A | BC) b. Find P(BC | A). (Do not round intermediate calculations. Round your answer to 3 decimal places.) P(BC A) c. Are A and B independent events? Yes because PAI B = PA) Yes because PAN B)0 No because P(A I B)PA). No because PAN B)0
7. Two random variables X and Y have joint probability density function s(x, y) = $(1 – xy), 0<x< l; 0<y<l. The marginal pdfs for X and Y are respectively S(x) = {(2-x) 0<x< 1; s()= (2-y) 0<y<l. Determine the conditional expectation E(Y|X = x) and hence determine E(Y) [7] (ii) [3] Verify your answer to part (i) by calculating the value of E(Y) directly from the marginal pdf for Y. [Total 10]
1. (10 pts) Consider two events, A and B, for which we have the following probabilities. P(A)=0.5 P(B) = 0.2 P(AB) 0.7 A. Find the probability P( AB) B. Find the probability P(AUB)
Consider two random variables X and Y be the proportion of time that a person travels to work by bus and MTR respectively (there are other modes as well). Moreover, X and Y has the following joint distribution f(x,y) 24xy, 0 x f(x,y)-0 otherwise 1,0 y 1, x + y 1 () Find the marginal distributions g(x) and h(y) respectively. (ii) Find the conditional density function fxly) (ii Ifit is known that a person has 0.75 chance of using bus,...
Consider a pair of discrete random variables X and Y. suppose that the marginal distribution of X is given by the table below. x 0.20 0.80 Suppose furthermore that the conditional distributions of tables below... given X are given by the two y0.20 0.80 0.60 0.40 Enter the joint probability mass function of X and Y into the table below .r Enter the joint probability mass function of X and Y into the table below. Check
Problem 1. Consider the two data collections (x,..-, X) and (y,. ya). The median difference statistic is the median of the (v-x) differences for the mn possible (x, y.) pairings, i= 1, ..., mandj = 1, . . ., n. Construct two specific data collections (x,. Xm) and (y,. .. V) that demonstrate that the median difference statistic is not equal to the difference in the separate medians for the two collections Problem 2. A Venn diagram is a graphical...
4. Suppose that a two-dimensional random vector (X, Y) has a joint probability density function as 0.48y(2-x), 0 1,0 x y x f(x,y)- 0, otherwise Find two possible marginal probability functions fx(x) and fy(y) of X and Y, respectively.
4. Suppose that a two-dimensional random vector (X, Y) has a joint probability density function as 0.48y(2-x), 0 1,0 x y x f(x,y)- 0, otherwise Find two possible marginal probability functions fx(x) and fy(y) of X and Y, respectively.
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....