Consider a random variable X, that takes values 0 and 1 with probabilities P(0) = P(1) = 0.5. Then, X = 0 with probability 0.5 and X = 1 with probability 0.5. What is the expected value of X?
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Consider a random variable X, that takes values 0 and 1 with probabilities P(0) = P(1)...
Consider a random variable X with the following probability mass function P(X=0)=0.25, P(X=5)=0.5, P(X=12)=0.25. What is the expected value (or mean) of X?
The Bernoulli random variable takes values 0 and 1, and has probability function f(x) = px (1 − p)1−x(a) By calculating f(0) and f(1), give a practical example of a Bernoulli experiment, and a Bernoulli random variable. (b) Calculate the mean and variance of the Bernoulli random variable.
A discrete random variable A takes values {1, 2, 4} with probabilities specified as follows: P[A = 1] = 0.5, P[A = 2] = 0.3 and P [A = 4] = 0.2 Given A= ), a discrete random variable N is Poisson distributed with rate equal to 1, that is: 9 P[N = n|A = 1] = in n! el Hint If N is Poisson distributed with rate 1, its expectation and variance are as follows: E[N] = Var [N]...
The random variable X takes only the values 0, ±1, ±2. In addition, it is known that P(-1 <X <2) 0.2 P(X = 0) = 0.05 PCI 1) = 0.35 P(X 2) = P(X = 1 or-1) (a) Find the probability distribution of X (b) Compute E[X]
Recall that a Bernoulli random variable with parameter p is a random variable that takes the value 1 with probability p, and the value 0 with probability 1 - p. Let X be a Bernoulli random variable with parameter 0.7. Compute the expectation values of X, denoted by E[X*1, for the following three values of k: k = 1,4, and 3203. E [X] = E [X4 E [X3203
(2 points) Consider a random variable X that takes the values 0, 50, 100, 150, and 200, each with probability 0.2. Let Y = |X − 100| be the (absolute) deviation of X from its average value 100. Compute the probability mass function (PMF) and cumulative distribution function (CDF) of Y . Explain.
Let X be a random variable that takes values x = (xi,... , xn) with respec- tive probabilities p (pi,. .. , pn). Write two R functions mymean (x,p) and myvariance (x, p), which find the mean and variance of X, respec- tively. Use your function to find the mean and variance of the point value of a random Scrabble tile, as in Example 4.1 Let X be a random variable that takes values x = (xi,... , xn) with...
Suppose X is a random variable taking on possible values 1,2,3 with respective probabilities.4, .5, and .1. Y is a random variable independent from X taking on possible values 2,3,4 with respective probabilities .3,.3, and 4. Use R to determine the following. a) Find the probability P(X*Y = 4) b) Find the expected value of X. c) Find the standard deviation of X. d) Find the expected value of Y. e) Find the standard deviation of Y. f) Find the...
(1 point) If X is a binomial random variable, compute the probabilities for each of the following cases: (a) P(X < 1), n = 7, p = 0.3 Probability = (b) P(X > 5), n = 7, p = 0.1 Probability = (C) P(X < 6), n = 8, p = 0.5 Probability = (d) P(X > 2), n = 3, p = 0.5 Probability =
2) Consider a random variable with the following probability distribution: P(X = 0) = 0.1, P(X=1) =0.2, P(X=2) = 0.3, P(X=3) = 0.3, and P(X=4)= 0.1. A. Generate 400 values of this random variable with the given probability distribution using simulation. B. Compare the distribution of simulated values to the given probability distribution. Is the simulated distribution indicative of the given probability distribution? Explain why or why not. C. Compute the mean and standard deviation of the distribution of simulated...