(1) Suppose the pdf of a random variable X is 0, otherwise. (a) Find P(2 < X < 3). (b) Find P(X < 1). (e) Find t such that P(X <t) = (d) After the value of X has been observed, let y be the integer closest to X. Find the PMF of the random variable y U (2) Suppose for constants n E R and c > 0, we have the function cr" ifa > 1 0, otherwise (a)...
5. Suppose X a single observation from a population with a Beta(0,1) distribution. (a) Suppose we want to test Ho :0 <1 against H :0>1 an we use a rejection region of X > 1/2. Find the size and power function for this test. Sketch the power function. (b) Now suppose we want to test H, :0 = 1 against H :0 = 2. Find the most powerful level a test. (Is there a Theorem we can use?) (C) Is...
Engineering statistics
Given that X-B (5, 0.7), find the following: (a) the probability of failure (b) P(x=0) (c) P(X= 2) (d) P(x>1) (e) the variance
5. Suppose that the joint pdf of the random variables X and Y is given by - { ° 0 1, 0< y < 1 f (x, y) 0 elsewhere a) Find the marginal pdf of X Include the support b) Are X and Y independent? Explain c) Find P(XY < 1)
Suppose X ~ Beta(a, β) with the constants α,β > 0, Define Y- 1- X. Find the pdf of Y.
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
Suppose that the probability density function of X is f(x) {cx3 0 1< x < 5 otherwise where c is a constant. Find P(X < 2).
3. Suppose X ~ Beta(a, β) with the constants α, β > 0, Define Y- 1-X. Find the pdf of Y