Question

A) -Let x have a uniform distribution on the interval 0 to 10. Find the probability. P(6 < x < 9)

-Let x have a uniform distribution on the interval 0 to 10. Find the probability. P(x > 6)

-Let x have a uniform distribution on the interval 0 to 10. Find the probability. P(2.7 < x < 8.4)

-Let x have an exponential distribution with = 1. Find the probability. (Round your answer to four decimal places.) P(1 < x < 9)

-Let x have an exponential distribution with = 1. Find the probability. (Round your answer to four decimal places.) P(x < 1.6)

-Let x have an exponential distribution with = 0.1. Find the probability. (Round your answer to four decimal places.)P(x > 8)

-Let x have an exponential distribution with = 0.4. Find the probability. (Round your answer to four decimal places.) P(5 < x < 8)

-Let x have an exponential distribution with = 0.3.Find the probability. (Round your answer to four decimal places.) P(x < 3)

Answer 1

For a) P(6 < x < 9) = 3/10, b) P(x > 6) = 4/10, and c) P(2.7 < x < 8.4) = 5.7/10.

Step-by-step explanation:

a) For the uniform distribution on the interval 0 to 10, the probability P(6 < x < 9) can be found by calculating the difference between the upper and lower bounds: P(6 < x < 9) = 9 - 6 = 3/10.

b) The probability of P(x > 6) can be found by subtracting the lower bound from the maximum value: P(x > 6) = 10 - 6 = 4/10.

c) To find the probability P(2.7 < x < 8.4), subtract the lower bound from the upper bound: P(2.7 < x < 8.4) = 8.4 - 2.7 = 5.7/10.