An article: "Second Moment Reliability Evaluation vs. Monte Carlo Simulations for Weld Fatigue Strength (Quality and Reliability Engr. Intl., 2012: 887-896)" examines the use of

Use a uniform distribution with a = 0.20 and b = 4.25 for the diameter X of the welds (mm).

a) Find and plot the density function of X.

b) What is the probability that the diameter exceeds 3 mm?

c) What is the probability that the diameter is within 1 mm of the mean diameter?

d) With a satisfying the condition 0.2 < a < a + 1 < 4.5, what is the probability P(a < X < a + 1)?