A random variable X has a distribution p(X=k) = A / (k(k+1)), k = 1,2,...,4, where...

A random variable X has a distribution p(X=k) = A / (k(k+1)), k = 1,2,...,4, where A is an constant. Then compute the value of p(1<=X<=3)

The answer will be either: 2/3, 3/4, 5/6, or 15/16

A discrete random variable X is uniformly distributed among −1,0,...,12. Then, what is its PMF for k=−1,0,...,12

The answer will be either: p(X = k) = 1/12, 1/13, 1/14, or 1

Expert Solution

milcah answered 1 year ago

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.

The random variable X has an Exponential distribution with parameter beta= 5. The P(X > 18|X...

The random variable X has an Exponential distribution with parameter beta= 5. The P(X > 18|X > 12) is equal to

A geometric distribution has a pdf given by P(X=x) = p(1-p)^x, where x = 0, 1,...

A geometric distribution has a pdf given by P(X=x) = p(1-p)^x, where x = 0, 1, 2, ..., and 0 < p < 1. This form of the geometric starts at x = 0, not at x = 1. Given are the following properties: E(X) = (1-p)/p, and Var(X) = (1-p)/p^2 A random sample of size n is drawn; the data are X1, X2, ..., Xn. A. Derive the Fisher information function for the parameter p. B. Find the Cramér-Rao...

Given that xx is a random variable having a Poisson distribution, compute the following: (a) P(x=1)P(x=1) when...

Given that xx is a random variable having a Poisson distribution, compute the following: (a) P(x=1)P(x=1) when μ=4.5μ=4.5 P(x)=P(x)= (b) P(x≤8)P(x≤8)when μ=0.5μ=0.5 P(x)=P(x)= (c) P(x>7)P(x>7) when μ=4μ=4 P(x)=P(x)= (d) P(x<1)P(x<1) when μ=1μ=1 P(x)=P(x)=

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).

Question 1: Given the following probability distribution for a random variable X: x P(X=x) -2 0.30...

Question 1: Given the following probability distribution for a random variable X: x P(X=x) -2 0.30 -1 0.15 0 0.20 1 0.20 2 0.15 a) Explain two reasons why the above distribution is a valid probability distribution. b) Calculate μX and σX. c) Determine the cdf(X), and write it as an additional column in the table. d) Calculate P(−1<X≤3) . e) Draw a histogram that represents the probability distribution of X.

Let X be a random variable with the following probability distribution: Value x of X P(X=x) ...

Let X be a random variable with the following probability distribution: Value x of X P(X=x) 20 0.35 30 0.10 40 0.25 50 0.30 Find the expectation E (X) and variance Var (X) of X. (If necessary, consult a list of formulas.) E (x) = ? Var (X) = ?

The p.d.f of the binomial distribution random variable X with parameters n and p is f(x)...

The p.d.f of the binomial distribution random variable X with parameters n and p is f(x) = n x p x (1 − p) n−x x = 0, 1, 2, ..., n 0 Otherwise Show that a) Pn x=0 f(x) = 1 [10 Marks] b) the MGF of X is given by [(1 − p) + pet ] n . Hence or otherwise show that E[X]=np and var(X)=np(1-p).

If P(-2 < Z < k)=.6 , where Z is a standard normal random variable, then...

If P(-2 < Z < k)=.6 , where Z is a standard normal random variable, then k is... Select one: a. 0.195 b. 0.73 c. 0.55 d. -0.40

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