Answer:
(a) The value of f (0) is 0.3487.
(b) The value of f (2) is 0.1937.
(c) The value of P (X ≤ 2) is 0.9298.
(d) The value of P (X ≥ 1) is 0.6513.
(e) The value of E (X) is 1.
(f) The value of V (X) is 0.9 and <em>σ</em> is 0.9487.
Step-by-step explanation:
The random variable <em>X</em> follows a Binomial distribution with parameter <em>n</em> = 10 and <em>p</em> = 0.10.
The probability mass function of <em>X</em> is:
(a)
Compute the value of <em>f</em> (0) as follows:
f (0) = P (X = 0)
Thus, the value of f (0) is 0.3487.
(b)
Compute the value of <em>f</em> (2) as follows:
f (2) = P (X = 2)
Thus, the value of f (2) is 0.1937.
(c)
Compute the value of P (X ≤ 2) as follows:
P (X ≤ 2) = P (X = 0) + P (X = 1) + P (X = 2)
Thus, the value of P (X ≤ 2) is 0.9298.
(d)
Compute the value of P (X ≥ 1) as follows:
P (X ≥ 1) = 1 - P (X < 1)
= 1 - P (X = 0)
= 1 - 0.3487
= 0.6513
Thus, the value of P (X ≥ 1) is 0.6513.
(e)
Compute the expected value of <em>X</em> as follows:
Thus, the value of E (X) is 1.
(f)
Compute the variance of <em>X</em> as follows:
Compute the standard deviation of <em>X</em> as follows:
Thus, the value of V (X) is 0.9 and <em>σ</em> is 0.9487.