The current in a certain circuit as measured by an ammeter is a continuous random variable ?X ?with the following density function: a.? ?Graph the pdf and verify that the total area under the density curve is indeed 1. b. Calculate P(X ? 4). How does this probability compare to P(X < 4)? c.? ?Calculate P(3.5 ? X ? 4.5) and also P( 4.5 < X).

Solution : Step 1: Here the current in a certain circuit as measured by an ammeter is a continuous random variable X , with density function We have to verify that the total area under the density curve is indeed 1. And the probabilities for different intervals of X. Step 2 : a) We have to verify that the total area under the density curve is indeed 1. By using the density function we can verify this That is 5 2 5 5 0.075x + 0.2 dx = 0.075[x /2] 3 + 0.2 [x] 3 3 = 0.075*8+ 0.2*2 = 1 So it's satisfying the property of the density curve. We can a line graph of pdf by using the values X f(x) 3 0.425 4 0.5 5 0.5