Question

Example 11.4. Assume that a car will be in good condition 90% of the time and in bad condition 10% of the time. Thus, P(G) = 0.90 and P(B) = 0.10. If X is a random variable representing the number of good cars at a given time, i.e., X = 0,1,2, or 3. Compute expected value, variance and skewness of probability distribution.

Answer 1

good condition 90% - Oolo of the time and in bad condition 10% P(x=00) = new piqen Sol? A care will be in of the time. This P(G)=0.90 P (B) = 0.10 że P( success) = 0.90 and P (failure) - time he x 2001, 2, 00 3. Here n23 Foro binoming distoni Intion P (X=D) = 3 ex Cox (0.90°.(0:0) 1. þ=0.90 ;q=0.10 x is a random vortable representing the number of good cares at a given 2 3.0 w 1x1x 1 = 0.001 P(x = 1) = 36 2 (6,99)'e (6.20 = 3x 0.90x0ool 20.027 P(x=2) = 362 X (6.90) x (0.10) 3 .* 6.90) + (0-10) 0,243

3-3 and PCM = 3) = 3 (0.90 (aroje as 1. (0.90 0.729 Probability disforibrition is siven by X 2 3. o 0.729 P(x) 0.001 0.027 0.243 " Expect value, 3 E (x1= Zalog ol 19 -Com 0.001) + ( 1 X 0.027) + (2x0, 243) + (3 (340170 0+ 0.027 + 0.486+21187 13 217 Variance a vor (x) v E (*) - [E (*)] Stine - (212) 0 +0.027)+ (2*x0.248) + (3 x 0.229) - (7.29) (

: vare (*) a.o22 а. 172 + 5 6 (29) 1.5G - 7.29 - О, 2 1 Сиди, 5 9 - Р npq 4. То — о. Чо О. Гох 3. Зох 3 с - С. 8 0.5 1 62 — 1,5 ч (Approx)