Find the expected value, μ, and standard deviation, σ, for a binomial random variable with each of the following values of n and p. (Round all answers for σ to four decimal places.) (a) n = 50, p = 1/2. μ = σ =
(b) n = 300, p = 1/4. μ = σ =
(c) n = 1000, p = 1/5. μ = σ =
(d) n = 1, p = 0.3. μ = σ =
(e) n = 20, p = 2/5. μ = σ =
Ans:
We know that
mean,=np
standard deviation,=sqrt(np(1-p))
e.g. for a)n=50,p=0.5
mean=np=50*0.5=25
standard deviation=sqrt(50*0.5*0.5)=3.5355
n | p | mean | std. dev. | |
a | 50 | 0.5 | 25 | 3.5355 |
b | 300 | 0.25 | 75 | 7.5000 |
c | 1000 | 0.2 | 200 | 12.6491 |
d | 1 | 0.3 | 0.3 | 0.4583 |
e | 20 | 0.4 | 8 | 2.1909 |
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