Let X be a random variable with density function:

f(x) = x if x ∈ (0, 1]

2 − x if x ∈ (1, 2]

0 the rest

Determine the distribution and density functions of the random variables:

a) Y = X + 1;

b) Y = −1/2X;

c) Y = X^2;

Apipe with an outside diameter of 15 cm is exposed to an ambient air and surrounding temperature of -20°c. the pipe has an outer surface temperature of 65°c and an emissivity of 0.85. if the rate of heat loss from the pipe surface is 0.95 kw per meter of length, the external convective heat transfer coefficient (h) is: (a) 12.5 w/m"k (b) 18.6 w/mk (c) 23.7 w/mk (d) 27.9 w/mk (e) 33.5 w/mk