Problem 5: A continuous random variable X is uniformly distributed between 0 and 10. a) Determine the expression for the probability density function for this random variable. (b) Determine the following: F(2) ii. F(2 < X < 10) iii. F(2 < X < 12) iv. F(X < 4) v. F(X > 4) vi. F(X = 4) vii. F(X > 4) Problem 6: A probability density function for a continuous random variable X is given by f(x) = k for 2 < X < 6 and zero otherwise. What is k? What is P(2 < X < 5)? What is P(X = 4)? d. Evaluate the cumulative distribution function (CDF) at x = 10, i.e. find F(X = 10).
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So, the expression for the probability density function is: $$ f_X(x) = \begin{cases} \frac{1}{10} & \text{for } 0 \leq x \leq 10 \\ 0 & \text{otherwise} \end{cases} $$ Show more…
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