1. Consider the Continuous Distribution Given by its Probability Density Function x-10 x € [10, 30] 200 f(x) = 0 x [10, 30] C. Compute the following using the CDF given above 1. P(x > 20) II. P( 15 < x < 25) III. P(x > 15 | x < 25)
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![1. Consider the Continuous Distribution Given by its Probability Density Function
\[ f(x) = \begin{cases}
\frac{x - 10}{200} & x \in [10, 30] \\
0 & x \notin [10, 30]
\end{cases} \]
C. Compute the following using the CDF given above
I. P( x > 20)
II. P( 15 < x < 25)
III. P( x > 15 | x < 25 )](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F15077d0c-06b0-46d9-ae2e-319ac77cceb5%2Fd6f57690-453f-47e9-b5dd-c487cb587913%2F31jbenk_processed.jpeg&w=3840&q=75)
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- Provide the solution and answer to the continuous problem.11. Let X be a continuous random variable with probability density function r>0 f(x)= 0, otherwise, where 1> 0. Let Y be the largest integer less than or equal to X. Determine the probability function of Y.Q2. The probability density function of X is as follows. f(x) = 2 - 2x, for x = [0, 1] Which one of the following expressions can be used to find P(0.5 < X < 1.5)? F(x) is the cumulative distribution function of X. (A) 1 - F(0.5) (C) F (1.5)-f(0.5) (B) f(1.5)-f(0.5) (D) 1.5 (2 - 2x) dx (E) other
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