A random variable X has range {0,1,2}; its expectation is 2/3 and its variance is 5/9. Determine the probability generating function of X and sketch its graph on the interval [0, 1].
Graph of pgf
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A random variable X has range {0,1,2}; its expectation is 2/3 and its variance is 5/9....
A value=2
A -2 It is known that for a random variable X, the Expectation of X equals 5, and that the Variance equals 7. A random variable Y is defined as: Y= AX+2A = (INSERT THE VALUE OF A) 3(a) Find the Expectation of Y 3(b) Find the Variance of Y 3(c) Find E[Y) 3(d) Find the Standard Deviation of Y Question 4 (10%) For the following probability density function. What is the probability P(x>0.? SÅ (1-x) -A<x<A
Let X be normally distributed random variable with expectation 5 and variance 16. Determine the values of c and d such that, Y := d + cX falls between [9, 11] with probability 0.95.
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O RANDOM VARIABLES AND DISTRIBUTIONS Expectation and variance of a random variable Let X be a random variable with the following probability distribution: Value x of X P(X-) 0.35 0.40 0.10 0.15 10 0 10 20 Find the expectation E (X) and variance Var(X) of X. (If necessary, consult a list of formulas.) Var(x) -
Verify the linearity of expectation: if X is a discrete random
variable (with a finite range), and its expectation is defined as
where f is the probability mass function of X. prove that E =
[X+Y]=E[X]+E[Y],andE[cX]=cE[X] for any real number c.
E[x] => + f(x) T
5. A discrete random variable, X, has three possible results with the following probabilities: Pr [X 2 /3 No other results can occur. (a) Sketch a graph of the probability function (b) What is the mean or expected value of this random variable? (c) What are the variance and standard deviation of this random variable?
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P7
continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The absolutely continuous random 0<r<3 and 0 elsewhere). Let (1 - if 0<x< 1, g(x) = (- 1)3 if 1<x<3, elsewhere. Calculate the pdf of Y = 9(X). P. 6 The absolutely continuous random variables X and Y have the joint probability density function fx.ya, y) = 1/(x?y?) if x > 1,y > 1 (and 0 elsewhere). Calculate the joint pdf of U = XY...
1. The random variable X is Gaussian with mean 3 and variance 4; that is X ~ N(3,4). $x() = veze sve [5] (a) Find P(-1 < X < 5), the probability that X is between -1 and 5 (inclusive). Write your answer in terms of the 0 () function. [5] (b) Find P(X2 – 3 < 6). Write your answer in terms of the 0 () function. [5] (c) We know from class that the random variable Y =...
Write code that when you are given the range and probability distribution of a random variable X. (i.e X ="the number of heads showing on 2 flipped fair coins": range = (0,1,2) probability distribution: [.25, .5, .25] Such that the code returns the expected value, standard deviation, and variance of the random variable . thanks!