The experiment is flipping a fair coin twice Let A be the event the first toss...
5. Toss a fair coin twice. A is the event "two tails", and B is the event "two heads". Are A and B mutually exclusive? Are they exhaustive? Evaluate P(AUB).
On a single toss of a fair coin, the probability of heads is 0.5 and the probability of tails is 0.5. If you toss a coin twice and get heads on the first toss, are you guaranteed to get tails on the second toss? Explain.Explain why – 0.41 cannot be the probability of some event.Explain why 1.21 cannot be the probability of some event.Explain why 120% cannot be the probability of some event.Can the number 0.56 be the probability of...
1. A fair coin is tossed three times. Let A be the event that there are at least two heads in the three tosses and let B be the event that there are exactly two heads among the three tosses. a. Draw the complete tree diagram for this experiment. [3] b. What are the sample space and probability function for this experiment? [5] c. Compute P(A), P(B), P(A|B), and P(B|A). [7]
1. A fair coin is tossed three times. Let A be the event that there are at least two heads in the three tosses and let B be the event that there are exactly two heads among the three tosses. a. Draw the complete tree diagram for this experiment. [3] b. What are the sample space and probability function for this experiment? [5] c. Compute P(A), P(B), P(A|B), and P(B|A). [7]
4. Toss a fair coin 6 times and let X denote the number of heads that appear. Compute P(X ≤ 4). If the coin has probability p of landing heads, compute P(X ≤ 3) 4. Toss a fair coin 6 times and let X denote the number of heads that appear. Compute P(X 4). If the coin has probability p of landing heads, compute P(X < 3).
1. A fair coin is tossed three times. Let A be the event that there are at least two heads in the three tosses and let B be the event that there are exactly two heads among the three tosses. a. Draw the complete tree diagram for this experiment. [3] b. What are the sample space and probability function for this experiment? (5) c. Compute P(A), P(B), P(A|B), and P(BA). [7] 2. Let U be a continuous random variable with...
A fair coin is tossed twice. Let X and Y be random variables such that: -X = 1 if the first toss is heads, and X = 0 otherwise. -Y = 1 if both tosses are heads, and Y = 0 otherwise. Determine whether or not X and Y are independent. So far, I have determined the the joint probability distribution as follows: x = 0 x = 1 y = 0 2/4 1/4 y = 1 0 1/4
A fair coin is tossed 3 times. Let X denote a 0 if the first toss is a head or 1 if the first toss is a zero. Y denotes the number of heads. Find the distribution of X. Of Y. And find the joint distribution of X and Y.
Toss a fair coin 4 times. Let Y be the number of heads. (a) What is the probability mass function of Y ? Compare your answer to the probability mass function of Binomial distribution. (b) What is the cumulative distribution function of Y ? (c) What is the expected value of Y ? (d) What is the variance of Y?
Suppose you flip three fair, mutually independent coins. Define the following events: Let A be the event that the first coin is heads. Let B be the event that the second coin is heads. Let C be the event that the third coin is heads. Let D be the event that an even number of coins are heads. Determine the probability space for this experiment (build the probability tree). Using the probability tree, find the probability of each of the...