Question

In: Statistics and Probability

A coin is tossed with P(heads) = p. a) What is the expected number of tosses...

A coin is tossed with P(heads) = p.

a) What is the expected number of tosses required to get n heads?

b) Determine the variance of the number of tosses needed to get the first head.

c) Determine the variance of the number of tosses needed to get n heads.

Solutions

Expert Solution

orchestra answered 2 years ago
Next > < Previous

Related Solutions

A coin is tossed with P(heads) = p. a) What is the expected number of tosses...
A coin is tossed with P(heads) = p. a) What is the expected number of tosses required to get n heads? b) Determine the variance of the number of tosses needed to get the first head. c) Determine the variance of the number of tosses needed to get n heads.
A coin with P[Heads]= p and P[Tails]= 1p is tossed repeatedly (the tosses are independent). Define...
A coin with P[Heads]= p and P[Tails]= 1p is tossed repeatedly (the tosses are independent). Define (X = number of the toss on which the first H appears, Y = number of the toss on which the second H appears. Clearly 1X<Y. (i) Are X and Y independent? Why or why not? (ii) What is the probability distribution of X? (iii) Find the probability distribution of Y . (iv) Let Z = Y X. Find the joint probability mass function
Suppose that you tossed a coin 1000 times in which 560 of the tosses were heads...
Suppose that you tossed a coin 1000 times in which 560 of the tosses were heads while 440 were tails. Can we reasonably say that the coin is fair? Justify your answer. Hint: use the concept of p-values. To evaluate the resulting probability, use an approximation by way of the CLT. Why does this offer a good approximation? Use a z-table or R to evaluate the N(0,1) cdf.
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)...
Let X be the number of heads in two tosses of a fair coin. Suppose a...
Let X be the number of heads in two tosses of a fair coin. Suppose a fair die is rolled X+1 times after the value of X is determined from the coin tosses. Let Y denote the total of the face values of the X+1 rolls of the die. Find E[Y | X = x] and V[Y | X = x] as expressions involving x. Use these conditional expected values to find E[Y] and V[Y].
A coin that lands on heads with a probability of p is tossed multiple times. Each...
A coin that lands on heads with a probability of p is tossed multiple times. Each toss is independent. X is the number of heads in the first m tosses and Y is the number of heads in the first n tosses. m and n are fixed integers where 0 < m < n. Find the joint distribution of X and 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).
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 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.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT