The pth percentile (0 < p < 100) of a random variable X is a number...

The pth percentile (0 < p < 100) of a random variable X is a number m that satisfies FX(m) = p/100. Find the 25th , 50th (median), and 75th percentiles of the exponential random variable with parameter λ. Find the same for a normal random variable with mean µ and standard deviation σ.

Expert Solution

milcah answered 3 months ago

Let X be a Bin(100, p) random variable, i.e. X counts the number of successes in...

Let X be a Bin(100, p) random variable, i.e. X counts the number of successes in 100 trials, each having success probability p. Let Y = |X − 50|. Compute the probability distribution of Y.

1. Let X be random variable with density p(x) = x/2 for 0 < x<...

1. Let X be random variable with density p(x) = x/2 for 0 < x < 2 and 0 otherwise. Let Y = X^2−2. a) Compute the CDF and pdf of Y. b) Compute P(Y >0 | X ≤ 1.8).

Calculate the variance of random variable X if P(X = a) = p= 1 -P(X =...

Calculate the variance of random variable X if P(X = a) = p= 1 -P(X = b).

Let X be a random variable such that P(X = 1) = 0.4 and P(X =...

Let X be a random variable such that P(X = 1) = 0.4 and P(X = 0) = 0.6. Compute Var(X).

Given a binomial random variable with n = 100 and p = .5, estimate the Pr[X...

Given a binomial random variable with n = 100 and p = .5, estimate the Pr[X ≥ 40]

A probability distribution function P(x) for a random variable X is defined by P(x) = P...

A probability distribution function P(x) for a random variable X is defined by P(x) = P r{X ≤ x}. Suppose that we draw a list of n random variables X1, X2, X3 · · · Xn from a continuous probability distribution function P that is computable in O(1) time. Give an algorithm that sorts these numbers in linear average case time.

a random variable X has the following pmf: X -1 0 1 P[X] 0.25 0.5 0.25...

a random variable X has the following pmf: X -1 0 1 P[X] 0.25 0.5 0.25 Define Y = X2 & W= Y+2. Which one of the following statements is not true? V[Y] = 0.25. E[XY] = 0. E[X3] = 0. E[X+2] = 2. E[Y+2] = 2.5. E[W+2] = 4.5. V[X+2] = 0.5. V[W+2] = 0.25. P[W=1] = 0.5 X and W are not independent.

Suppose that random variable X 0 = (X1, X2) is such that E[X 0 ] =...

Suppose that random variable X 0 = (X1, X2) is such that E[X 0 ] = (µ1, µ2) and var[X] = σ11 σ12 σ12 σ22 . (a matrix) (i) Let Y = a + bX1 + cX2. Obtain an expression for the mean and variance of Y . (ii) Let Y = a + BX where a' = (a1, a2) B = b11 b12 0 b22 (a matrix). Obtain an expression for the mean and variance of Y . (ii)...

Assume that x is a binominal random variable with n=100 and p=0.40. Use a normal approximation...

Assume that x is a binominal random variable with n=100 and p=0.40. Use a normal approximation to find the following: a) P(x≥38) b) P(x=45) c) P(x>45) d) P(x<45)

QUESTION 1 If Z is a standard normal random variable, then P(Z > 0) = 0...

QUESTION 1 If Z is a standard normal random variable, then P(Z > 0) = 0 1 0.4579 0.5 1 points QUESTION 2 Company A claims that 20% of people in Sydney prefer its product (Brand A). Company B disputes the 20% but has no idea whether a higher or lower proportion is appropriate. Company B randomly samples 400 people and 88 of them prefer Company A's product (Brand A). Assuming a 5% significance level, which one of the following...

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