Question

5. Suppose a random variable X follows exponential distribution with X ~ exp(1). (a) Determine the boundaries of the probability P(X ? 5) using Markov's inequality. (b) Determine the boundaries of the probability P(X ? 5) using Cantelli's inequality. (c) Determine the exact value of the probability P(X? 5) using the probability density function of X.

          5. Suppose a random variable X follows exponential distribution with X ~ exp(1).
(a) Determine the boundaries of the probability P(X ? 5) using Markov's inequality.
(b) Determine the boundaries of the probability P(X ? 5) using Cantelli's inequality.
(c) Determine the exact value of the probability P(X? 5) using the probability density
function of X.

5. Suppose a random variable X follows exponential distribution with X exp(1).
(a) Determine the boundaries of the probability P(X ? 5) using Markov's inequality.
(b) Determine the boundaries of the probability P(X ? 5) using Cantelli's inequality.
(c) Determine the exact value of the probability P(X? 5) using the probability density
function of X.

Added by Steven A.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Hoan Nguyen

03/21/2024

Step 1

For an exponential distribution with parameter $\lambda = 1$, the expected value is $E[X] = \frac{1}{\lambda} = 1$. Therefore, $P(X \ge 5) \le \frac{1}{5} = 0.2$. Since $P(X \ge 5)$ is a probability, it must be between 0 and 1. Thus, the boundaries are $0 \le P(X Show more…

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5. Suppose a random variable X follows exponential distribution with $X \sim exp(1)$. (a) Determine the boundaries of the probability $P(X \ge 5)$ using Markov's inequality. (b) Determine the boundaries of the probability $P(X \ge 5)$ using Cantelli's inequality. (c) Determine the exact value of the probability $P(X \ge 5)$ using the probability density function of X.