Two fair dice are rolled. Find (In tabular form) the joint and marginal probability mass functions of X and Y when a. X is the largest value obtained on two dice and Y is the sum of the values. Compute P(Y 2X = 0); b. X is the value on the first die and Y is the larger of the two values. Compute P(Y>= X); c. X is the smallest and Y is the largest value obtained on the dice.

Roll two dice. Let X be the value on the first die and let Y be the value on the second die. Then both X and Y take values 1 to 6 a) Write the full joint probability table b) Compute the marginal pmf of X and of Y. c) Are X and Y independent?

a, b, d,

A fair coin is tossed repeatedly until head appears for the third time. Calculate the mean and variance of the total number of tails that show up. Let X be the random variable that denotes the total number of tails that show up. Write down the probability mass function and cumulative distribution function of X.

help please answer in text form with proper workings and explanation for each and every part and steps with concept and introduction no AI no copy paste remember answer must be in proper format with all working

Choose ALL THE CORRECT STATEMENTS in the following ones about probability distribution. i. Probability mass function indicates the probability distribution of a continuous random variable. ii. Probability mass function indicates the probability distribution of a discrete random variable. iii. The probability mass function of a discrete random variable X at a is denoted by P(X < a). iv. The probability function of a continuous random variable Y can be described by using P(Y= a).

I need part d) ONLY

Consider rolling 2, 3-sided dice. Let X = the sum of the dice. Let Y = the product of the dice. a. Find the joint probability function for X and Y. b. Find the marginal probability functions for X and Y. Find P(X > 3|Y = 3) C.

Suppose that Y. .., Y, are i.i.d. random variables with a N(uy, o) distribution. How would the probability density of Y change as the sample size n increases? Hint: Think about the law of large numbers. HY: A. As the sample size increases, the variance of Y decreases. So, the distribution of Y becomes less concentrated around B. As the sample size increases, the variance of Y increases. So, the distribution of Y becomes less concentrated around uy. O C. As the sample size increases, the variance of Y decreases. So, the distribution of Y becomes highly concentrated around uy. O D. As the sample size increases, the variance of Y increases. So, the distribution of Y becomes highly concentrated around uy.

Suppose that X and Y have following joint probability distribution: F(x,y) X 2 1 0.10 y 3 0.20 5 0.10 a.) Find the marginal distribution of X. b.) Find the marginal distribution of Y. LO 4 0.15 0.30 0.15