Q–2: [5+2+3 Marks] Let X be a random variable giving the number of heads minus the...

Q–2: [5+2+3 Marks] Let X be a random variable giving the number of
heads minus the number of tails in three tosses of a coin.
a) Find the probability distribution function of the random variable X.
b) Find P(−1 ≤ X ≤ 3).
c) Find E(X).

Expert Solution

orchestra answered 2 years ago

Let W be a random variable giving the number of heads minus the number of tails...

Let W be a random variable giving the number of heads minus the number of tails in three independent tosses of an unfair coin where p = P(H) = 1 3 , and q = P(T) = 2 3 . (a) List the elements of the sample space S for the three tosses of the coin and to each sample point assign a value of W. (b) Find P(−1 ≤ W < 1). (c) Draw a graph of the probability...

Let X be the random variable for the number of heads obtained when three fair coins...

Let X be the random variable for the number of heads obtained when three fair coins are tossed: (1) What is the probability function? (2) What is the mean? (3) What is the variance? (4) What is the mode?

Let X be a random variable that is equal to the number of times a 5...

Let X be a random variable that is equal to the number of times a 5 is rolled in three rolls of a fair 5-sided die with the integers 1 through 5 on the sides. What is E[X2 ]? What is E2 [X], that is, (E[X])2 ? Justify your answers briefly

Two coins are tossed at the same time. Let random variable be the number of heads...

Two coins are tossed at the same time. Let random variable be the number of heads showing. a) Construct a probability distribution for b) Find the expected value of the number of heads.

What is the probability that the random variable X (which is the number of Heads from...

What is the probability that the random variable X (which is the number of Heads from flipping a coin 5 times) is equal to 0?

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.

1) Define a random variable in words. (e.g. X = number of heads observed) 2) Specify...

1) Define a random variable in words. (e.g. X = number of heads observed) 2) Specify the distribution of the random variable including identifying the value(s) of any parameter(s). (e.g. X ∼ Binomial(10.5)) 3) State the desired probability in terms of your random variable (e.g. P(X < 3)). 4) Calculate the desired probability (e.g. P(X < 3) = .055). [Note: You may need more than 1 random variable per question.] 1. If the amount of time a lightbulb lasts in...

Let X be the number of heads and let Y be the number of tails in...

Let X be the number of heads and let Y be the number of tails in 6 flips of a fair coin. Show that E(X · Y ) 6= E(X)E(Y ).

Let X be the random variable representing the number of calls received in an hour by...

Let X be the random variable representing the number of calls received in an hour by a 911 emergency service. A probability distribution of X is given below. Value of X 0 1 2 3 4 Probability P(x) 0.32 ____ ____ 0.16 0.08 (a) Suppose the probability that X = 1 and the probability that X = 2 are the same. What are these probabilities? Incorrect: Your answer is incorrect. (b) What is the probability that at least one call...

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

Question