Consider a random variable X with probability density function
\(f(x) = \begin{cases} 3/x^4,for & x ≥ 1 \\ 0,& otherwise \\ \end{cases}\).
Find mean and variance.

A) \$E(X)=2/5,Var(X) = 4/7\$
B) \$E(X)=1/7,Var(X) = 2/5\$
C) \$E(X)=4/6,Var(X) = 2/5\$
D) \$E(X)=3/2,Var(X) = 3/4\$

If x is a continuous random variable whose P.D.F.is given by
\(f(x) = \begin{cases} k(5x-2x^2),for & 0≤x≤2 \\ 0,& otherwise \\ \end{cases}\)
Then P(x > 1) is

A) \$14/25\$
B) \$12/27\$
C) \$17/28\$
D) \$11/24\$

Consider a random variable X with probability density function
\(f(x) = \begin{cases} 2x,for & 0≤x≤1 \\ 0,& otherwise \\ \end{cases}\).
Find mean and variance.

A) \$E(X)=3/2,Var(X) = 2/15\$
B) \$E(X)=2/3,Var(X) = 1/18\$
C) \$E(X)=2/3,Var(X) = 2/15\$
D) \$E(X)=3/2,Var(X) = 1/18\$

Let X be a random variable with P.D.F
\(f(x) = \begin{cases} cx(5-x),for & 0≤x≤5 \\ 0,& otherwise \\ \end{cases}\).
find the value of c,P(2 ≤ X ≤ 3)

A) \$c=6/125,0.296\$
B) \$c=6/25,0.297\$
C) \$c=6/125,0.257\$
D) \$c=6/625,0.242\$

TUConn students have designed the new U-phone. They have determined that the lifetime of a U-Phone is given by the random variable X (measured in hours), with probability density function.
\(f(x) = \begin{cases} 10/x^2,for & x≥10 \\ 0,& x≤10 \\ \end{cases}\)
Find the probability that the u-phone will last more than 20 hours.

A) \$1/4\$
B) \$1/8\$
C) \$1/2\$
D) \$2/3\$