Flip a fair coin 4 times. Let ? and ? denote the number of heads and...

Flip a fair coin 4 times. Let ? and ? denote the number of heads and tails correspondingly.

(a) What is the distribution of ?? What is the distribution of ? ?
(b) Find the joint PMF. Are ? and ? independent?

(c) Calculate ?(? ?) and ?(X≠?)(d) Calculate C??(?, ? ) and C???(?, ? )

Solutions

Expert Solution

milcah answered 8 months ago

Next > < Previous

Related Solutions

Flip a fair coin 100 times. Let X equal the number of heads in the first...

Flip a fair coin 100 times. Let X equal the number of heads in the first 65 flips. Let Y equal the number of heads in the remaining 35 flips. (a) Find PX (x) and PY (y). (b) In a couple of sentences, explain whether X and Y are or are not independent? (c) Find PX,Y (x, y).

A fair coin is tossed four times. Let X denote the number of heads occurring and...

A fair coin is tossed four times. Let X denote the number of heads occurring and let Y denote the longest string of heads occurring. (i) determine the joint distribution of X and Y (ii) Find Cov(X,Y) and ρ(X,Y).

Q7 A fair coin is tossed three times independently: let X denote the number of heads...

Q7 A fair coin is tossed three times independently: let X denote the number of heads on the first toss (i.e., X = 1 if the first toss is a head; otherwise X = 0) and Y denote the total number of heads. Hint: first figure out the possible values of X and Y , then complete the table cell by cell. Marginalize the joint probability mass function of X and Y in the previous qusetion to get marginal PMF’s.

A fair coin is tossed r times. Let Y be the number of heads in these...

A fair coin is tossed r times. Let Y be the number of heads in these r tosses. Assuming Y=y, we generate a Poisson random variable X with mean y. Find the variance of X. (Answer should be based on r).

a) A coin is tossed 4 times. Let X be the number of Heads on the...

a) A coin is tossed 4 times. Let X be the number of Heads on the first 3 tosses and Y be the number of Heads on the last three tossed. Find the joint probabilities pij = P(X = i, Y = j) for all relevant i and j. Find the marginal probabilities pi+ and p+j for all relevant i and j. b) Find the value of A that would make the function Af(x, y) a PDF. Where f(x, y)...

HOMEWORK-You flip a coin FOUR times. Let H = Number of Heads. Calculate: (a) P (H...

HOMEWORK-You flip a coin FOUR times. Let H = Number of Heads. Calculate: (a) P (H = 4) = (b) P (H ≥ 1) = (c) P (H < 4) = (d) P (1 < H ≤ 4) = HINT: GET YOUR SAMPLE SPACE. Leave your answers EITHER as a simplified fraction ( e.g. 4/16 = 1/4 when simplified) OR a decimal rounded to FOUR decimal places. Also do not forget to enter your leading zero when entering decimals. CAUTION: FOLLOW...

Every day you flip a fair coin four times and if it is heads all four...

Every day you flip a fair coin four times and if it is heads all four times, you give a dollar to charity. In a year with 365 days, what is your expected annual donation to charity and what is the variance?

1. Flip a fair coin ten times. Find the probability of at least seven heads. 2....

1. Flip a fair coin ten times. Find the probability of at least seven heads. 2. Draw five cards at once from a deck. Find the probability of getting two pairs. 3. Roll a die infinitely times. Find the probability that you see an even number before you see an one. 4. You and your friend take turns to draw from an urn containing one green marble and one hundred blue marbles, one at a time and you keep the...

A coin is tossed twice. Let Z denote the number of heads on the first toss...

A coin is tossed twice. Let Z denote the number of heads on the first toss and W the total number of heads on the 2 tosses. If the coin is unbalanced and a head has a 40% chance of occurring, find the correlation between W and Z.

A coin is tossed twice. Let Z denote the number of heads on the first toss...

Subjects