4.1 For f( x) = N(20, 49) find;

1. P [ x ? 30],

2. P[ x ? 30],

3. P[15 ? x ? 30].

4.2 Prove that the coefficient of the exponential density function of equation 4.5 must be .

4.3 Particles from a radioactive device arrive at a detector at the average rate of 3 per second. The time of arrival can be described by an exponential pdf with b .

1. What is the probability that no more than 2 seconds will elapse before a particle is detected?

2. What is the probability that one has to wait between 2 and 5 seconds for a detection?

4.4 A Rayleigh pdf is defined over the range x ? 0 as

For a = 2, what is P[4 ? x ? 10]?

4.5 Assume that the radii of the paint droplets in Figure 4.2 can be described by an exponential pdf with b = 4.1. What is the probability that the radii are greater than 20 microns?

4.6 In a certain production line 1000 ohm ( ?) resistors that have a 10% tolerance are being manufactured. The resistance is described by a normal distribution with m = 1000 ? and ? = 40 ?. What fraction will be rejected?

4.7 The probability of dying from an amount of radiation is described by a normal random variable with a mean...