Question

The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution function egin{equation} f(x) = egin{cases} 1 - frac{1}{e^{8x}}, & x ge 0\ 0, & ext{elsewhere} end{cases} end{equation} Find the probability of waiting less than 12 minutes between successive speeders a. using the cumulative distribution function of X. b. using the probability density function of X. c. Find the expectation E[X] and Var(X) of the random variable X.

          The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution function
egin{equation*}
f(x) = egin{cases} 1 - frac{1}{e^{8x}}, & x ge 0\ 0, & 	ext{elsewhere} end{cases}
end{equation*}
Find the probability of waiting less than 12 minutes between successive speeders
a. using the cumulative distribution function of X.
b. using the probability density function of X.
c. Find the expectation E[X] and Var(X) of the random variable X.

$The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution function eginequation* f(x) = egincases 1 - frac1e^8x, x ge 0 0, extelsewhere endcases endequation* Find the probability of waiting less than 12 minutes between successive speeders a. using the cumulative distribution function of X. b. using the probability density function of X. c. Find the expectation E[X] and Var(X) of the random variable X.$

Added by Eric U.

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