Question

In: Statistics and Probability

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).

Solutions

Expert Solution


Related Solutions

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).
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).
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 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.
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).
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.
Let X be the number of Heads when we toss a coin 3 times. Find the...
Let X be the number of Heads when we toss a coin 3 times. Find the probability distribution (that is, the probability function) for X
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...
STAT 2332 #1. A coin is tossed 1000 times, it lands heads 516 heads, is the...
STAT 2332 #1. A coin is tossed 1000 times, it lands heads 516 heads, is the coin fair? (a) Set up null and alternative hypotheses (two tailed). (b) Compute z and p. (c) State your conclusion. #2. A coin is tossed 10,000 times, it lands heads 5160 heads, is the coin fair? (a) Set up null and alternative hypotheses (two tailed). (b) Compute z and p. (c) State your conclusion.
1. Four coins are tossed 11 times. The number of heads is counted and the following...
1. Four coins are tossed 11 times. The number of heads is counted and the following data is reported: 4, 3, 2, 0, 3, 3, 1, 2, 3, 2, 1. Calculate the following sample statistics. Be sure to provide a formula for your answer. a. Sample mean? b. Sample median? c. Sample mode? d. Sample range? e. Sample variance?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT