Question

Q3. Random variable X takes value from 0 to 10 and follows a continuous uniform distribution such that $X sim ext{Unif}(0, 10)$ and the probability density function is $f(x) = frac{1}{10}, quad 0 < x < 10$. Answer the following questions. Q3-(a). [10 pts.] What's the mean ($mu$) and variance ($sigma^2$) of X? mean: , variance: (four decimal places) Q3-(b). [10 pts.] Compute a lower bound (minimum) of $P(mu - 1.5sigma < X < mu + 1.5sigma)$ using Chebyshev's Inequality. Compute the answer to four decimal places.

          Q3. Random variable X takes value from 0 to 10 and follows a continuous uniform distribution such that
$X sim 	ext{Unif}(0, 10)$
and the probability density function is
$f(x) = frac{1}{10}, quad 0 < x < 10$.
Answer the following questions.
Q3-(a). [10 pts.] What's the mean ($mu$) and variance ($sigma^2$) of X?
mean: , variance: (four decimal places)
Q3-(b). [10 pts.] Compute a lower bound (minimum) of $P(mu - 1.5sigma < X < mu + 1.5sigma)$ using Chebyshev's Inequality. Compute the answer
to four decimal places.

$Q3. Random variable X takes value from 0 to 10 and follows a continuous uniform distribution such that X sim extUnif(0, 10) and the probability density function is f(x) = frac110, quad 0 < x < 10. Answer the following questions. Q3-(a). [10 pts.] What's the mean (mu) and variance (sigma^2) of X? mean: , variance: (four decimal places) Q3-(b). [10 pts.] Compute a lower bound (minimum) of P(mu - 1.5sigma < X < mu + 1.5sigma) using Chebyshev's Inequality. Compute the answer to four decimal places.$

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