Consider the random variable X which can take on three values a − b, a, and a + b for real numbers a and b with b > 0. Moreover,
P{X =a−b}=P{X =a+b} and P{X =a−b}=2P{X =a}.
(a) Find the variance of X.
(b) Find the cumulative distribution function of X.
Consider the random variable X which can take on three values a − b, a, and...
(10 points) Consider a discrete random variable X, which can only take on non-negative integer values, with E[Xk] = 0.8, k = 1,2, .... Use the moment generating function approach to find the pmf of Px(k), k = 0,1,....
Let x be a continuous random variable with a uniform distribution. x can take on values between x=20 and x=54. Compute the probability, P(26<x<39). P(26<x<39)= ? (Give at least 3 decimal places) Let x be a continuous random variable with a uniform distribution. x can take on values between x=13 and x=52. Compute the probability, P(27<x<36). P(27<x<36)= ? (Give at least 3 decimal places)
5. Let X be a discrete random variable. The following table shows its possible values r and the associated probabilities P(X -f(x) 013 (a) Verify that f(x) is a probability mass function (b) Calculate P(X < 1), P(X < 1), and P(X < 0.5 or X > 2). (c) Find the cumulative distribution function of X ompute the mean and the variance of
please 6 and 7 6. (3.18, 20) A continuous random variable X that can assume values between r = 2 and x = 5 has a density function given by f(x) = 2(1+x)/27. Find the Cumulative Distribution Function F(x). 7. (3.14) The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with a cumulative distribution function x<0, F(x) = -e-41, x20 Find the probability of waiting between 3 to 7 minutes a)...
Let X be a standard normal distribution. Let ξ be another random variable, independent of X, which can take only two possible values, say -1 and 1. Moreover, assume that Ele] = 0. ( . (b) Find COV(x,Y). (c) Are X and Y independent? (d) Is the pair (X,Y) bivariate normal? a) Find the distribution of Y -£X Let X be a standard normal distribution. Let ξ be another random variable, independent of X, which can take only two possible...
3x+1 # 6 Given that f(x) is a probability distribution for a random variable that can take on 50 the values x = 1,2,3,4,5, find an expression for the cumulative distribution function F(x) of the random variable. 15
1. Suppose that X and Y are random variables that can only take values in the intervals 0 X 2 and 0 Y 3 2. Suppose also that the joint cumulative distribution function (cdf) of X and Y, for 0 < 2 and 03 y 3 2, is as follows: Fy). 16 [5] (a) Determine the marginal cdf Fx(x) of X and the marginal cdf Fy () of Y [5] (b) Determine the joint probability density function (pdf) f(x, y)...
5. Let X be a discrete random variable. The following table shows its possible values associated probabilities P(X)( and the f(x) 2/8 3/8 2/8 1/8 (a) Verify that f(x) is a probability mass function. (b) Calculate P(X < 1), P(X 1), and P(X < 0.5 or X >2) (c) Find the cumulative distribution function of X. (d) Compute the mean and the variance of X.
Problem 1. (6pt) A discrete random variable X can take one of three different values z1, z and z probabilities ¼, ½ and ¼ respectively, and another random variable Y can 1. 32 and ys, also with probabilities 4V2 and /4, respectively, as shown in the the relative frequency with which some of those values are jointly taken is also shown in the following table with take one of three distinct values P2 P14 (a) (Spt) From the data given...
Question 1 A continuous random variable X which represents the amount of sugar (in kg) used by a family per week, has the probability density function c(x-102-x) 1sxs2 ; otherwise (0) (ii) (ii) Determine the value of c. Obtain cumulative distribution function Find P(X < 1.2). Consider the following cumulative distribution function for X. 06 0.8 1.0 Fx) 0.9 (i) Determine the probability distribution. (ii) Find P(X 1). (ii) Find P(OX5) Question 3 Consider the following pdf otherwise (i) (ii)...