SOLUTION: Answer the following questions for a continuous random variable X with density function given below 𝑓(𝑥) =1/2, 𝑓𝑜𝑟 1 ≤ 𝑥 ≤ 3 A. Calculate the probab

Question 1159326: Answer the following questions for a continuous random variable X with density function given below
𝑓(𝑥) =1/2, 𝑓𝑜𝑟 1 ≤ 𝑥 ≤ 3
A. Calculate the probability for random variable X 𝑃(𝑋 ≤ 1.6)
B. Derive the cumulative distribution function F(x)
C. Use the cumulative distribution function F(x) to evaluate P(2 < X < 2.5)
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
this is a uniform function with pdf f(x)=1/(b-a)
the cumulative distribution function is
0 for x<=1
(x-a)/(b-a) for 1 < x<3 (integrate the pdf (1/b-a) between a and b or 1 and 3
1 for x>=3
probability x <= 1.6 is 0.6/2.0 or 30%
probability of the second (doesn't format when I write it mathematically) is 0.5/2.0 or 25%

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