Question

2. The waiting time, in minutes, between successive speeders spotted by a radar unit is a continuous random variable $X in mathbb{R}$ with cumulative distribution function egin{equation} F(x) = egin{cases} 0 & ext{if } x le 2, \ 1 - frac{16}{x^4} & ext{if } x ge 2. end{cases} end{equation} (a) Find the probability density function of X. (b) Find the probability that the waiting time between successive speeders is more than 4 minutes but less than 8 minutes (i) using the cumulative distribution function of X, (ii) using the probability density function of X. (c) Find the expected waiting time between successive speeders.

          2. The waiting time, in minutes, between successive speeders spotted by a radar unit is a continuous random variable $X in mathbb{R}$ with cumulative distribution function
egin{equation*}
F(x) = egin{cases} 0 & 	ext{if } x le 2, \ 1 - frac{16}{x^4} & 	ext{if } x ge 2. end{cases}
end{equation*}
(a) Find the probability density function of X.
(b) Find the probability that the waiting time between successive speeders is more than 4 minutes but less than 8 minutes
(i) using the cumulative distribution function of X,
(ii) using the probability density function of X.
(c) Find the expected waiting time between successive speeders.

$2. The waiting time, in minutes, between successive speeders spotted by a radar unit is a continuous random variable X in mathbbR with cumulative distribution function eginequation* F(x) = egincases 0 extif x le 2, 1 - frac16x^4 extif x ge 2. endcases endequation* (a) Find the probability density function of X. (b) Find the probability that the waiting time between successive speeders is more than 4 minutes but less than 8 minutes (i) using the cumulative distribution function of X, (ii) using the probability density function of X. (c) Find the expected waiting time between successive speeders.$

Added by Dylan H.

Question

Please give Ace some feedback