Consider the following discrete probability distribution: X -0.99 0.48 0.71 1.4 P(X) 0.1 0.4 0.3 0.2...

Question

Question

Consider the following discrete probability distribution:

X	-0.99	0.48	0.71	1.4
P(X)	0.1	0.4	0.3	0.2

a) What is E[X]?

Round your answer to at least 3 decimal places.

b) What is Var[X]?

Round your answer to at least 3 decimal places.

Answer 1

Answer #1

a)
E[X] = sum(X*P(X))
= -0.99*0.1 + 0.48*0.4 + 0.71*0.3 + 1.4*0.2
= 0.586

b)
Var[X] = sum((X - E[X])^2*P(X))
= (-0.99 - 0.586)^2*0.1 + (0.48 - 0.586)^2*0.4 + (0.71 - 0.586)^2*0.3 + (-0.99 - 1.4)^2*0.2

= 1.400

Answer 2

Similar Homework Help Questions

Consider the following probability distribution: x P(x) 1 0.1 2 ? 3 0.2 4 0.3 What...

Consider the following probability distribution: x P(x) 1 0.1 2 ? 3 0.2 4 0.3 What must be the value of P(2) if the distribution is valid? A. 0.6 B. 0.5 C. 0.4 D. 0.2 What is the mean of the probability distribution? A. 2.5 B. 2.7 C. 2.0 D. 2.9
Consider the probability distribution shown below: X 10 12 18 20 p(x) 0.2 0.3 0.1 0.4...

Consider the probability distribution shown below: X 10 12 18 20 p(x) 0.2 0.3 0.1 0.4 Find the standard deviation of X.
Consider the following data: P(X=x) | 0.3 | 0.2 | 0.1 | 0.2 | 0.2 Step...

Consider the following data: P(X=x) | 0.3 | 0.2 | 0.1 | 0.2 | 0.2 Step 1 of 5: Find the expected value E). Round your answer to one decimal place

2. Consider a random variable with the following probability distribution: P(X=0) = 0.1, P(X=1) = 0.2,...

2. Consider a random variable with the following probability distribution: P(X=0) = 0.1, P(X=1) = 0.2, P(X=2) = 0.4, and P(X=3) = 0.3 a. Find P(X<=1) b. Find P(1<X<=3)
5.Consider a discrete random variable X with the probability mass function xp(x) Consider Y-g(X) 0.2 0.4...

5.Consider a discrete random variable X with the probability mass function xp(x) Consider Y-g(X) 0.2 0.4 0.3 0.1 a)Find the probability distribution of Y b) Find the expected value of Y, E(Y) Does μ Y equal to g(μx)? 4
Consider the following data: x 3 4 5 6 7 P(X=x) 0.1 0.3 0.3 0.1 0.2...

Consider the following data: x 3 4 5 6 7 P(X=x) 0.1 0.3 0.3 0.1 0.2 Step 3 of 5: Find the standard deviation. Round your answer to one decimal place. Step 4 of 5: Find the value of P(X>4). Round your answer to one decimal place. Step 5 of 5: Find the value of P(X≤6). Round your answer to one decimal place.

Consider the following data: x 5 6 7 8 9 P(X=x)P(X=x) 0.3 0.1 0.1 0.3 0.2...

Consider the following data: x 5 6 7 8 9 P(X=x)P(X=x) 0.3 0.1 0.1 0.3 0.2 Copy Data Step 1 of 5 : Find the expected value E(X). Round your answer to one decimal place.
Consider the following data: x 1 2 3 4 5 P(X=x) 0.2 0.1 0.1 0.2 0.4...

Consider the following data: x 1 2 3 4 5 P(X=x) 0.2 0.1 0.1 0.2 0.4 Step 5 of 5 : Find the value of P(X≤1). Round your answer to one decimal place
A discrete random variable X has probability mass function P() 0.1 0.2 0.2 0.2 0.3 Use...

A discrete random variable X has probability mass function P() 0.1 0.2 0.2 0.2 0.3 Use the inverse transform method to generate a random sample of size from the distribution of X. Construct a relative frequency table and compare the empirical with the theoretical probabilities. Repeat using the R sample function. 1000

Consider the following data: x 0 1 2 3 4 P(X=x) 0.1 0.2 0.2 0.3 0.2...

Consider the following data: x 0 1 2 3 4 P(X=x) 0.1 0.2 0.2 0.3 0.2 Step 4 of 5 : Find the value of P(X>3) . Round your answer to one decimal place.