Question

In: Statistics and Probability

LetXbe a discrete random variable with the following PMF: P(X=x) = 0.3 for x = 1,...

LetXbe a discrete random variable with the following PMF:

P(X=x) =

0.3 for x = 1,

a for x = 2,

0.5 for x= 3,

0 otherwise

(a) Find the value of a.

(b) Find Fx(x), the CDF of X.

(c) What is the value of Fx(2)?

(d) Find E[X].

(e) FindE[X^2].

(f) Find V ar(X)

----------------------

A certain area of the eastern United States is, on average,hit by 2 hurricanes a year. Find the probability that the area will be hit byexactly 3 hurricanes in a given year.

Solutions

Expert Solution

orchestra answered 1 year ago
Next > < Previous

Related Solutions

A discrete random variable named X has the following pmf (probability mass function): X P(x) 1...
A discrete random variable named X has the following pmf (probability mass function): X P(x) 1 0.6 3 0.2 7 0.1 11 0.1 17a) Find P(X>6) 17b) What is the probability two independent observations of X will both equal 1? 17c) Find the population mean also known as E(X)= the expected value of 17d) Find the population variance of X with both the “regular” formula and “convenient” formula Make a table and show your work. You should get the same...
a. Suppose that X is a discrete random variable with pmf f(x) = (2 + θ(2...
a. Suppose that X is a discrete random variable with pmf f(x) = (2 + θ(2 − x))/ 6 , x = 1, 2, 3, where the parameter θ belongs to the parameter space Ω = (θ : −2 < θ < 2). Suppose further that a random sample X1, X2, X3, X4 is taken from this distribution, and the four observed values are {x1, x2, x3, x4} = {3, 2, 3, 1}. Find the maximum likelihood estimate of θ....
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.
1. The probability mass function of a discrete random variable X is defined as p(x) =...
1. The probability mass function of a discrete random variable X is defined as p(x) = ax for x = 1, 2, 4, 8 (p(x) =0 for all other values) then the value of a is? 2. Let X be a discrete random variable with Var(X) =6.0 and E(X2) = 17.00. Then: E(X) = ? 3. If X is a binomial random variable with parameters n and p, i.e. X ~ b(x; n, p), then the expected value of X...
Let X be a binomial random variable with n = 11 and p = 0.3. Find...
Let X be a binomial random variable with n = 11 and p = 0.3. Find the following values. (Round your answers to three decimal places.) (a)     P(X = 5) (b)     P(X ≥ 5) (c)     P(X > 5) (d)     P(X ≤ 5) (e)     μ = np μ = (f)    σ = npq σ =
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).
For a discrete random variable X, it is known that Pr[X = 1] = 0.15, Pr[X...
For a discrete random variable X, it is known that Pr[X = 1] = 0.15, Pr[X = 3] = 0.3, Pr [X = 5] = 0.35, and Pr[X = 7] = 0.2. Find Pr[X < 5].
Consider a Bernoulli random variable X such that P(X=1) = p. Calculate the following and show...
Consider a Bernoulli random variable X such that P(X=1) = p. Calculate the following and show steps of your work: a) E[X] b) E[X2] c) Var[X] d) E[(1 – X)10] e) E[(X – p)4] f) E[3x41-x] g) var[3x41-x]
1 point) If xx is a binomial random variable, compute P(x)P(x) for each of the following...
1 point) If xx is a binomial random variable, compute P(x)P(x) for each of the following cases: (a)  P(x≤1),n=5,p=0.3P(x≤1),n=5,p=0.3 P(x)=P(x)= (b)  P(x>3),n=4,p=0.1P(x>3),n=4,p=0.1 P(x)=P(x)= (c)  P(x<3),n=7,p=0.7P(x<3),n=7,p=0.7 P(x)=P(x)=
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT