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) = 3 + x 2 − y 2 , for 1 ≤ x ≤ 3 and 0 ≤ y ≤ 1 0 otherwise

Expert Solution

As it hasn't been given that the coin is fair or not so we assume the probability of Heads on the coin to be =

The images below contain the complete solution, so check them out..

orchestra answered 2 years ago

A coin is tossed 6 times. Let X be the number of Heads in the resulting...

A coin is tossed 6 times. Let X be the number of Heads in the resulting combination. Calculate the second moment of X. (A).Calculate the second moment of X (B). Find Var(X)

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).

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).

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 coin with probability p>0 of turning up heads is tossed 4 times. Let X be...

A coin with probability p>0 of turning up heads is tossed 4 times. Let X be the number of times heads are tossed. (a) Find the probability function of X in terms of p. (b) The result above can be extended to the case of n independent tosses (that is, for a generic number of tosses), and the probability function in this case receives a very specific name. Find the name of this particular probability function. Notice that the probability...

A coin is tossed three times. X is the random variable for the number of heads...

A coin is tossed three times. X is the random variable for the number of heads occurring. a) Construct the probability distribution for the random variable X, the number of head occurring. b) Find P(x2). c) Find P(x1). d) Find the mean and the standard deviation of the probability distribution for the random variable X, the number of heads occurring.

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???(?, ? )

4 fair coins are tossed. Let X be the number of heads and Y be the...

4 fair coins are tossed. Let X be the number of heads and Y be the number of tails. Find Var(X-Y) Solution: 3.5 Why?

If a fair coin is tossed 25 times, the probability distribution for the number of heads,...

If a fair coin is tossed 25 times, the probability distribution for the number of heads, X, is given below. Find the mean and the standard deviation of the probability distribution using Excel Enter the mean and round the standard deviation to two decimal places. x P(x) 0 0 1 0 2 0 3 0.0001 4 0.0004 5 0.0016 6 0.0053 7 0.0143 8 0.0322 9 0.0609 10 0.0974 11 0.1328 12 0.155 13 0.155 14 0.1328 15 0.0974 16 ...

Suppose a coin is tossed 100 times and the number of heads are recorded. We want...

Suppose a coin is tossed 100 times and the number of heads are recorded. We want to test whether the coin is fair. Again, a coin is called fair if there is a fifty-fifty chance that the outcome is a head or a tail. We reject the null hypothesis if the number of heads is larger than 55 or smaller than 45. Write your H_0 and H_A in terms of the probability of heads, say p. Find the Type I...

Question