Consider the following PMF for a continus random variable f(x) = 0,25-Kx®2 Calculate K Calculate P(3<x<5)...
Consider the following PDF for a continus random variable f(x) X: 0 x<0,4 Calculate K Calculate P0, 1<x<0,3) Calculate P(X <= 0,2) Calculate E(X) Calculate Var(X) 3,75-Kx®2]
1. Given f(x) = kx(9 - x2)4 0<x<3, otherwise a) Find k. f(x) 20 a pdf pro b) Calculate F(x) and the three quartiles. c) Calculate E(X2) and Var(x2). d) Calculate E(X) and Var(x). (needs more than calc 1) (Bonus)
Given f(x) k(1 + x2) 2. -1 < x< 2 a) Find k. b) Calculate F(x) and the three quartiles. c) Calculate E(X), Var(X)
5. Let X be a discrete random variable with the following PMF: for x = 0 Px(x)- for 1 for x = 2 0 otherwise a) Find Rx, the range of the random variable X. b) Find P(X21.5). c) Find P(0<X<2). d) Find P(X-0IX<2)
2. For a discrete random variable X, with CDF F(X), it is possible to show that P(a < X S b)-F(b) - F(a), for a 3 b. This is a useful fact for finding the probabil- ity that a random variable falls within a certain range. In particular, let X be a random variable with pmf p( 2 tor c-1,2 a. Find the CDF of X b. Find P(X X 5). c. Find P(X> 4). 3. Let X be a...
he cumulative distribution function (cdf), F(z), of a discrete ran- om variable X with pmf f(x) is defined by F(x) P(X < x). Example: Suppose the random variable X has the following probability distribution: 123 45 fx 0.3 0.15 0.05 0.2 0.3 Find the cdf for this random variable
Exercise 2 Consider a random variable X with E]5 and VarX 16 (a) Calculate P(lz-5 < 6) if X follows a normal distribution. (b) Use Chebyshev's inequality to provide a lower bound for P(-5). (No longer assume X is normal.)
Problem 3. The random variable X has density function f given by 0, elsewhere (a) Assuming that 6 0.8, determine K (b) Find Fx(t), the c.d.f. of X (c) Calculate P(0.4 <X < 0.8)
1. Consider the following function: 4x 0<x<0.5 f(x)= 4- kx 0.5 <x<1 0 Otherwise a) (5%) Determine k such that f(x) is a probability density function. b) (6%) Determine CDF of x. c) (4%) Using CDE, what is the p(x 0.75) d) (4%) Using CDE what is p(x<0.6) e) (4%) Determine E(x) Type here to search o TT
26. Let the random variable Y have pmf f(y) = 5(6/y, where y = 1, 2, 3, . . . Compute E(Y). [HINT: for Irl < 1 we have Σ zrz = r/(1-r)2]