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).

Expert Solution

x p xp x²p

1 0.4 0.4 0.4

0 0.6 0 0

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

Total 0.4 0.4

So,

E(X) = 0.4

Var(X) = E(X²) - (E(X))²

= 0.4 - 0.4² = 0.24

So,

Answer is:

0.24

milcah answered 5 months ago

Let ? be a binomial random variable with ? = 9 and p = 0.4. Find:...

Let ? be a binomial random variable with ? = 9 and p = 0.4. Find: ?(?>6) ?(?≥2) ?(2≤?<5) ?(2<?≤5) ?(?=0) ?(?=7) ?? ?2

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).

Let X be a Bin(n, p) random variable. Show that Var(X) = np(1 − p). Hint:...

Let X be a Bin(n, p) random variable. Show that Var(X) = np(1 − p). Hint: First compute E[X(X − 1)] and then use (c) and (d). (c) Var(X) = E(X^2 ) − (E X)^ 2 (d) E(X + Y ) = E X + E Y

(a) Let X be a binomial random variable with parameters (n, p). Let Y be a...

(a) Let X be a binomial random variable with parameters (n, p). Let Y be a binomial random variable with parameters (m, p). What is the pdf of the random variable Z=X+Y? (b) Let X and Y be indpenednet random variables. Let Z=X+Y. What is the moment generating function for Z in terms of those for X and Y? Confirm your answer to the previous problem (a) via moment generating functions.

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 binomial random variable with n=7 and p=0.7. Find the following. P(X =...

Let x be a binomial random variable with n=7 and p=0.7. Find the following. P(X = 4) P(X < 5) P(X ≥ 4)

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) = ?

Let X represent the standard normal random variable. The P{X > 2.07} is equal to:

1. (Use Computer) Let X represent a binomial random variable with n = 400 and p...

1. (Use Computer) Let X represent a binomial random variable with n = 400 and p = 0.8. Find the following probabilities. (Round your final answers to 4 decimal places.) Probability a. P(X ≤ 330) b. P(X > 340) c. P(335 ≤ X ≤ 345) d. P(X = 300) 2. (Use computer) Suppose 38% of recent college graduates plan on pursuing a graduate degree. Twenty three recent college graduates are randomly selected. a. What is the...

To test ?0: p = 0.4; ?1: p ≠ 0.4, a simple random sample of size...

To test ?0: p = 0.4; ?1: p ≠ 0.4, a simple random sample of size n = 1000 is obtained from a population such that ? ≤ 0.05?. (a) If x = 420 and n = 1000, compute the test statistic 0 z . (b) Test the hypothesis using (i) the classical approach and (ii) the P-value approach. Assume an ? = 0.01 level of significance. (c) What is the conclusion of the hypothesis test?

Question