Stores sell glass cup with box, 20s in each box. The probability that there is 0
ID: 3261249 • Letter: S
Question
Stores sell glass cup with box, 20s in each box. The probability that there is 0, 1, or 2 defective item in each box is 0.8, 0.1 or 0.1 respectively. A customer picks out a box and choose 4 to check from it. If all results are okay, then he buy this box. Find the probability that there is one defective item in the box. Consider two fair dice A and B. Die A is six-sided and is numbered 1 through to 6 whilst die B is four-sided and is numbered 1 through to 4. Both dice are rolled. Let X = A + B. Find the probability mass function and cumulative distribution function of X. Suppose X has a discrete uniform distribution: P(X = x_i) = 1/n, i = 1, 2, .., n. Find the distribution function of X. A random variable Z has the pmf below. (1) What is the value of a? (2) What is P(l lessthanorequalto ZExplanation / Answer
Q.2 Probability of getting one defective item in each box of 20 = 0.1
so Pr (of getting one item defective out of 4 = 4C1 (0.1)1 (0.9)3 = 0.2916
Q.3
Number of possibilities for A = 1,2,3,4,5,6
Number of possibilities for B = 1,2,3,4
X = A + B
X = 2,3,4,5,6,7,8,9,10
so f(X) = 1/24 ; X = 2
= 2/24; X =3
= 3/24 ; X = 4
= 4/24 ; X = 5
= 4/24; X = 6
= 4/24; X =7
= 3/24 ; X = 8
= 2/24; X = 9
= 1/24 ; X = 10
CDF of X
F(x) = 1/24 ; X = 2
= 3/24; X <=3
= 6/24 ; X <= 4
= 10/24 ; X <= 5
= 14/24; X <= 6
= 18/24; X <=7
= 21/24 ; X <= 8
= 23/24; X <= 9
= 1 ; X <= 10
Q.4 P (X = xi ) = 1/n ; i = 1,2,3,.....n
Distribution function of X is geometric distribution.
Q>5 P(3) = 1 - [ P(0) + P(1) + P(2) ] = 1 - (0.20 + 0.16 + 0.41) = 0.23
P ( 1 <=Z <3) = P(1) + P(2) = 0.16 + 0.41 = 0.57
FZ(1.7) = FZ (Z < 1.7) = P(0) + P(1) = 0.20 + 0.16 = 0.36
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