If a resistor with resistance R ohms carries a current of I amperes, the potential difference across the resistor, in volts, is given by V = IR. Suppose that I is lognormal with parameters μI = 1 and σ2I = 0.2, R is lognormal with parameters μR = 4 and σ2R = 0.1, and that I and R are independent.
a. Show that V is lognormally distributed, and compute the parameters μV and σ2V.
b. Find P(V < 200).
c. Find P(150 ≤ V ≤ 300).
d. Find the mean of V.
e. Find the median of V.
f. Find the standard deviation of V.
g. Find the 10th percentile of V.
h. Find the 90th percentile of V.