21.A uniform distribution has parameters a = 0.1 and B = 0.9. P(0.23 < X <...
a = 0.1 and B = 0.9. 21. A uniform distribution has parameters P(0.23 < X < 0.67) =
A uniform distribution has parameters alpha = 0.1 and beta = 0.9. P(0.23 < X < 0.67) = _______________________
17. Find the mean of X given Y = - The joint probability density function is f(x, y) for random variables X and Y. #x, y) = f (xy + y) 0<x<1,0<y<1 0 Elsewhere = 21. A uniform distribution has parameters a = 0.1 and B = 0.9. P(0.23 < X < 0.67) = 13. At a company, 75% of the employees pass a screening test to see if they need additional training. Of those that pass the screening test,...
Consider the following cumulative distribution function for X. 7 0.1 08 0.9 1.0 Fo) 0.3 0.6 (i) Determine the probability distribution. ii) Find P(X < 1). iii Find P(0 <XS5).
СТ 5. The triangular distribution has pdf 0<<1 f(x) = (2-2) 1<x<2. It is the sum of two independent uniform(0.1) random variables. (a) Find c so that f(x) is a density function. (b) Draw the pdf, and derive the cdf using simple geometry. (c) Derive the cdf from its definition. (d) Derive the mean and variance of a random variable with this distribution.
(a) Find P{X=2}
(b) Find P{X<2}
(c) Find P{2 <= X < 2.5}
The cumulative distribution of a random variable X is given as 0 x < 0 0<x<2 4 Fx(x) = 2<x<3 4 x 3 x + 1
3. Let X and Y have a bivariate normal distribution with parameters x -3 , μΥ 10, σ 25, 9, and ρ 3/5. Compute (c) P(7<Y < 16). (d) P(7 < Y < 161X = 2).
4. Suppose X has a discrete uniform distribution: the distribution function of X 5. A random variable Z has the pmf bclow. P (X-х,)-1 , is|2 n. Find 0 Pz(z) 0.20 0.16 0.4 a (1) What is thevalue of a ? (2) What is P(l S Z <3)? (3) What is Fz (1.7)? 6.
Central limit theorem 9. Suppose that a random variable X has a continuous uniform distribution fx(3) = (1/2,4 <r <6 o elsewhere (a) Find the distribution of the sample mean of a random sample of size n = 40. (b) Calculate the probability that the sample mean is larger than 5.5.
1 point) Suppose a random variable x is best described by a uniform probability distribution with range 2 to 5. Find the value of a that makes the following probability statements true. (a) P(x <a) -0.18 a E (b) P(x < a) 0.78 (c) P(x 2 a) 0.23 (d) P(x > a) = 0.95 a= (e) P( 1.78 x a) = 0.02 a=