Consider a binomial experiment with n = 10 and p = 0.10. (a) Compute f(0). If required, round your answer to four decimal places. (b) Compute f(2). If required, round your answer to four decimal places. (c) Compute P(x ≤ 2). If required, round your answer to four decimal places. (d) Compute P(x ≥ 1). If required, round your answer to four decimal places. (e) Compute E(x). (f) Compute Var(x) and σ. If required, round Var(x) answer to one decimal place and σ answer to four decimal places. Var(x) = σ =

For all asked probabilities you need to use a Binomial distribution table. Remember this table has the information of the cummulative probabilities P(X≤x).

a. f(0) ⇒ P(X=0) = 0.3487

b. f(2) ⇒ P(X=2) ⇒ P(X≤2) - P(X≤1) = 0.9298 - 0.7361 = 0.1937

c. P(X≤2) = 0.9298

d. P(X ≥ 1) = 1 - P(X ≤ 1) = 1 - 0.7361 = 0.2639

e. E(X)= nρ = 10*0.10 = 1

f. V(X)= nρ(1-ρ) = 10*0.1*0.9 = 0.9

σ= √V(X) = √0.9 = 0.9487

I hope it helps!

topeadeniran2 topeadeniran2 · Answer 2 · 2022-02-17T18:36:58+01:00

The binomial experiment depicts that f(0) will be 0.3487.

How to compute the binomial experiment

From the information given, it can be noted that:

n = 10

p = 0.10

q = 1 - 0.10 = 0.90

f(0) ⇒ P(X=0) = 0.3487

f(2) = P(X=2) ⇒ P(X≤2) - P(X≤1)

= 0.9298 - 0.7361

= 0.1937

P(X≤2) = 0.9298

P(X ≥ 1) = 1 - P(X ≤ 1)

= 1 - 0.7361 = 0.2639

E(X) = nρ

= 10 × 0.10 = 1

V(X) = nρ(1-ρ)

= 10 × 0.1 × 0.9

= 0.9

σ = √V(X) = √0.9

= 0.9487

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