Question

In: Statistics and Probability

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 answer with both

formulas. Finally, find the standard deviation.

Expert Solution

a)

P(X>6) = P(X=7) + P(X=11) = 0.1+0.1 = 0.2

b)

P(Two independent observations will both equal 1) = P(X=1) * P(X=1) = 0.6*0.6 = 0.36

c)

d)

Using convenient formula:

Using the standard formula:

X	p(X)	X * p(x)	X-E(x)	(X-E(x))^2	((X-E(x))^2)*p(x)
1	0.6	0.6	-2	4	2.4
3	0.2	0.6	0	0	0
7	0.1	0.7	4	16	1.6
11	0.1	1.1	8	64	6.4
				84	10.4

Var(X) =

Please do upvote if you are satisfied! Let me know in the comments if anything is not clear. I will reply ASAP!

orchestra answered 2 years ago

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...

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...

Consider a discrete random variable with the following probability mass function x 0 1 2 3...

Consider a discrete random variable with the following probability mass function x 0 1 2 3 4 5 p(x) 0.1 0.1 0.2 0.3 0.2 0.1 Generate a random sample of size n =10000 from this distribution. Construct a bar diagram of the observed frequencies versus the expected frequencies.(using R)

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.

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. 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....

1) A discrete random variable X has the following probability distribution: x 13 18 20 24...

1) A discrete random variable X has the following probability distribution: x 13 18 20 24 27 p(x) 0.22 0.25 0.2 0.17 0.16 Compute each of the following quantities (give the exact numbers): (a) P(18)= (b) P(X>18)= (c) P(X?18)= (d) The mean ? of X is (e) The variance ?2 of X is (write all decimal points) (f) The standard deviation ? of X is (use 4 decimal points) 2) Borachio works in an automotive tire factory. The number X...

1.Plotting densitiesPlot the probability mass function (pmf) or probability density function (pdf) for eachof the following...

1.Plotting densitiesPlot the probability mass function (pmf) or probability density function (pdf) for eachof the following scenarios:(a) Consider abinomialrandom variable,X.i. Plot the pmf ofX∼Bin(n= 10,p= 0.3).ii. Plot the pmf ofX∼Bin(n= 10,p= 0.7).iii. Plot the pmf ofX∼Bin(n= 100,p= 0.3).iv. What happens to the shape of the pmf ofX∼Bin(n,p) whenpgets larger?v. What happens whenngets larger?(b) Consider ageometricrandom variable,Y.i. Plot the pmf ofY∼Geom(p= 0.1).ii. Plot the pmf ofY∼Geom(p= 0.5).iii. Plot the pmf ofY∼Geom(p= 0.8).iv. What happens to the shape of the pmf ofY∼Geom(p)...

Let Y be a discrete random variable with probability mass function given by P(Y =i)=c·(i−2) fori=3,4,6...

Let Y be a discrete random variable with probability mass function given by P(Y =i)=c·(i−2) fori=3,4,6 1. Pay attention to the possible values for Y , and find the numerical value of c. Make sure to show work / justify your answer. 2. Draw the graph of the cumulative distribution function of Y.

Let f(x) = b(x+1), x = 0, 1, 2, 3 be the probability mass function (pmf)...

Let f(x) = b(x+1), x = 0, 1, 2, 3 be the probability mass function (pmf) of a random variable X, where b is constant. A. Find the value of b B. Find the mean μ C. Find the variance σ^2