6. Let X have a N(1,2) distribution. Using only the tables, find: a) P(X 1.5) b)...
8. Let X (i-1,2) be independent N(0,1) random variables. a. Find the value of c such that P ( (X1 + X2 )2/( X2 -X1)2 < c ) =.90 b. Find P(2 X1 -3 X2< 1.5) c. Find 95th percentile of the distribution of Y-2 X1 -3 X2
15 Let X and Y have a trinomial distribution with n = 8, P1 = 0.4 and P2 = 0.1 f (x,y) = 8! 10.4*0.190.58---8,0 < x + y < 8,2 € N, Y EN x!y! (8 - x - y)! (a) Find E (Y|X = x), Var (Y|X = x) (b) Compute E (XY)
6. Let X N (100, 25). Find the following: (a) P(X < 100) Answer: 1/2, (b) P(X> 100) Answer: 1/2, (c) P(X 100) Answer: 0, (d) the 99th percentile for this distribution Answer: approx 111.632. (5.4.2)
) 6. Let x be the binomial random variable with n = 10 and p = .9 (2) a. Find P(x = 8) (5) b. Create a cumulative probability table for the distribution. (2) c. Find P( x is less than or equal to 7) (2) d. Find P(x is greater than 7) e. Find the mean, μ. (1) f. Find the standard deviation, σ. (1) g. Find the variance. ...
Problem 1. 15 points] Let X be a uniform random variable in the interval [-1,2]. Let Y be an exponential random variable with mean 2. Assunne X and Y are independent. a) Find the joint sample space. b) Find the joint PDF for X and Y. c) Are X and Y uncorrelated? Justify your answer. d) Find the probability P1-1/4 < X < 1/2 1 Y < 21 e) Calculate E[X2Y2]
Let x be the binomial random variable with n=10 and p = 9 a. Find P(x = 8) and create a cumulative probability table for the distribution. b. Find P( x is less than or equal to 7) and P(x is greater than 7) c. Find the mean, u, the standard deviation, o, and the variance. d. Does the Empirical rule work on this distribution for data that is within one, two or three standard deviations of the mean? Explain....
Let X-Binomial(n = 10, p = 0.2). Find the mean of X. 01 Question 6 (1 point) LetX~Binomial(n = 100, p = 0.2). Find the standard deviation of X.
1. Let X have a Bernoulli distribution, where P(X 1-p and P(X 0 1-p. (a) For a random sample of size n = 10. test Ho : p $ versus H1 : p > 흘. Use 10 the critical region {ΣΧί 6) i. Find the power function, and sketch it. ii. What is the size of this test? (b) For a random sample of size n = 10: i. Find the most powerful test of Ho : p = 흘...
(2) Let Pn [x] = {p € P[x] : degp <n}, where P[x] is the set of all polynomials. Let the polynomials li() defined by II;tilt - a;) i=0,1,...11 bi(T) = 11: a; - aj) where aj, j = 0,1,..., are distinct real numbers and aia . Show that (d) The change of basis transformation from the standard basis ', j = 0,1,...,n to l; () is given by the Vandermonde matrix (1 00 ... am 1 01 .01 1...
Let X be a random variable satisfying P(-1 X 1) = 0.3, P(X = 1.5) = 0.1, P(1.5 X P(3 X 7.4) 0.3, P(X 10)0.2 2) = 0.2 Find (i) P(X 2 1.3) (ii) P(X 2.3) ii P(1.5< X 2) (iv) P(1.5 3X 38)