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.

Expert Solution

orchestra answered 1 year ago

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)...

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)

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.

An unbiased coin is tossed four times. Let the random variable X denote the greatest number...

An unbiased coin is tossed four times. Let the random variable X denote the greatest number of successive heads occurring in the four tosses (e.g. if HTHH occurs, then X = 2, but if TTHT occurs, then X = 1). Derive E(X) and Var(X). (ii) The random variable Y is the number of heads occurring in the four tosses. Find Cov(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).

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 ...

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).

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...

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...

An honest coin is tossed n=3600 times. Let the random variable Y denote the number of...

An honest coin is tossed n=3600 times. Let the random variable Y denote the number of tails tossed. Use the 68-95-99.7 rule to determine the chances of the outcomes. (A) Estimate the chances that Y will fall somewhere between 1800 and 1860. (B) Estimate the chances that Y will fall somewhere between 1860 and 1890.

Question