Please write in detail neatly. Kindly don't use any symbols andshortcut words. Please write the formula appropriately. Thequestion is:
Consider an unbiased 4-sided die where the sides are numbered 1,2, 3, 4, and a biased coin with probability of head P(H) =4 dividedby 7. A chance experiment consists of rolling the die once and thentossing the coins many times as the number showing on the die. LetX represent the outcome of the roll of the die, and let Y representthe number of heads observed after tossing the coin. Below, findeach of the following:
a. R(X) and R(Y)
b. Give the distribution of X. What is the name of thisdistribution?
c. What is the name of the conditional distribution P(Y | X =2). Give this distribution.
d. Give the conditional expectation E[Y | X = 2].
e. Give the joint distribution of the random vector < X, Y>.
f. Give P(Y = 3).
g. Give P(X = 2 | Y = 2).
h. Give E[E[Y|X]].
Please explain to me about \"unbiased 4-sided die\" and \"a biasedcoin.\" I just need to understand the meaning of them. Could youplease give two examples so that I can understand easily?
