Question

In: Statistics and Probability

A fair coin is tossed 3 times. Let X be equal to 0 or 1 accordingly...

A fair coin is tossed 3 times. Let X be equal to 0 or 1 accordingly as head or tail occurs on a first Toss. Let y equal to number of heads that occurs. Find

A) the distribution of X and Y

B) the joint distribution of X and Y

C) whether they are independent or not

D) the COV (XY)

Solutions

Expert Solution


Related Solutions

Suppose a fair coin is tossed 3 times. Let E be the event that the first...
Suppose a fair coin is tossed 3 times. Let E be the event that the first toss is a head and let Fk be the event that there are exactly k heads (0 ≤ k ≤ 3). For what values of k are E and Fk independent?
Suppose a fair coin is tossed 3 times. Let E be the event that the first...
Suppose a fair coin is tossed 3 times. Let E be the event that the first toss is a head and let Fk be the event that there are exactly k heads (0 ≤ k ≤ 3). For what values of k are E and Fk independent?
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).
1. A coin is tossed 3 times. Let x be the random discrete variable representing the...
1. A coin is tossed 3 times. Let x be the random discrete variable representing the number of times tails comes up. a) Create a sample space for the event;    b) Create a probability distribution table for the discrete variable x;                 c) Calculate the expected value for x. 2. For the data below, representing a sample of times (in minutes) students spend solving a certain Statistics problem, find P35, range, Q2 and IQR. 3.0, 3.2, 4.6, 5.2 3.2, 3.5...
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)...
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 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 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)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT