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

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orchestra answered 1 year ago

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).

Define the random variable X to be the number of times in the month of June...

Define the random variable X to be the number of times in the month of June (which has 30 days) Susan wakes up before 6am a. X fits binomial distribution, X-B(n,p). What are the values of n and p? c. what is the probability that Susan wakes us up before 6 am 5 or fewer days in June? d. what is the probability that Susan wakes up before 6am more than 12 times?

Let X represent the standard normal random variable. The P{X > 2.07} is equal to:

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.

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).

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...

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...

1) Let X be a normally distributed random variable with a standard deviation equal 3

1) Let X be a normally distributed random variable with a standard deviation equal 3; i.e. X∼N(μ, σ=3. Someone claims that μ=13. A random sample of 16 observations generate a sample mean of 14.56. a) Does the sample mean provide evidence against the above claim at 5% significance level? Complete the four steps of the test of hypothesis: b) Assume that X was not normal; for example, X∼Unifμ-3, μ+3 which would have the same standard deviation. Use simulation to...

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).

Let discrete random variable X be the number of flips of a biased coin required to...

Let discrete random variable X be the number of flips of a biased coin required to get tails, where P(tails) = 1/3 . a) Calculate the probability for every value of X from 1 to 10. b) Sketch a plot of the p.m.f. of X for the first 10 flips. c) Sketch a plot the c.d.f. of X for the first 10 flips.

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