1) Probability that A) P of X is less than or equal to 3, and grater than or equ

Question

1) Probability that A) P of X is less than or equal to 3, and grater than or equal to -1 B) E(X), V(X)?
2)Probability of no traffic fatalities in an hour? (Full question in pic)
1. (15 points) A random variable can take only values between-3 and 3, jactusive. The probability for each value is given by the rule 16 p(x) . (5) to.15)(1-035)(0.5625-s-2 125 2 (15 points) A large metropolitan area reports 2.4 traffic fatalities per day on average. (a) Determine the probability of no traffic fatalities in a given hour. (b) Probability of at least two traffic fatalities in an hour? 25s- (o.t) e 2! 3 (15 points) On a multiple choice exam, each question has exactly five options. Only one option is correct for each question. If the student is merely guessing at the answer, each option should be equally likely to be chosen. Given that the test has 18 questions and that a student is jub guessing on each question, find the probability of the following events: (a) Exactly three are correct. (b)More than 5 questions are correct 0.2 =0.2

Explanation / Answer

1)

a)

P(-1 < X <3) = P(X<=3) - P(X <= -1)

= 1 - P(X <= -1)

= 1 - P(X= -1) - P(X=-2) - P(X = -3)

= 1 - 3/16 - 2/16 - 1/16

= 10/16

= 5/8

E(X) = sum of (x * P(x))

= -3 * 1/16 + -2 * 2/16 + -1 * 3/16 + 0 * 4/16 + 1 * 3/16 + 2 * 2/16 + 3 * 1/16

= 0

E(X^2) = sum of( x^2 * P(X))

= 9 * 1/16 + 4 * 2/16 + 1 * 3/16 + 0 * 4/16 + 1 * 3/16 + 4 * 2/16 + 9 * 1/16

= 40/16

= 5/2

V(X) =E(X^2) - E(X)^2

= 5/2 - (5/8)^2

= 135/64

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