Mathematics, 21.02.2020 16:41, SaliJano8950

Discrete random variable X has the following probability distribution: x 13 18 20 24 27 P ( x ) 0.22 0.25 0.20 0.17 0.16 Compute each of the following quantities. P ( 18 ) . P(X > 18). P(X ≤ 18). The mean μ of X. The variance σ 2 of X. The standard deviation σ of X.

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answered: niyah2x3

(a) P(X = 18) = 0.25

(b) P(X > 18) = 0.53

(d) Mean = 19.76

(e) Variance = 22.2824

(f) Standard deviation = 4.7204

Step-by-step explanation:

We are given that discrete random variable X has the following probability distribution:

X P (x) X * P(x) $X^{2}$ $X^{2}$ * P(x)

13 0.22 2.86 169 37.18

18 0.25 4.5 324 81

20 0.20 4 400 80

24 0.17 4.08 576 97.92

27 0.16 4.32 729 116.64

(a) P ( X = 18) = P(x) corresponding to X = 18 i.e. 0.25

Therefore, P(X = 18) = 0.25

(b) P(X > 18) = 1 - P(X = 18) - P(X = 13) = 1 - 0.25 - 0.22 = 0.53

(d) Mean of X, $\mu$ = ∑X * P(x) ÷ ∑P(x) = (2.86 + 4.5 + 4 + 4.08 + 4.32) ÷ 1

= 19.76

(e) Variance of X, $\sigma^{2}$ = ∑ $X^{2}$ * P(x) - $(\sum X * P(x))^{2}$

= 412.74 - $19.76^{2}$ = 22.2824

(f) Standard deviation of X, $\sigma$ = $\sqrt{variance}$ = $\sqrt{22.2824}$ = 4.7204 .

answered: Guest

Its equal to d=7.07in

answered: Guest

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Discrete random variable X has the following probability distribution: x 13 18 20 24 27 P ( x ) 0.22...