Question

The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function.

f(x) =

0.025x + 0.4		3 ≤ x ≤ 5
0		otherwise

(a)

Graph the pdf.

Verify that the total area under the density curve is indeed 1.

5 0.025x + 0.4 dx 3	=	5 3
	=	2.3125 −
	=

(b)

Calculate

P(X ≤ 4).

How does this probability compare to

P(X < 4)?

P(X ≤ 4) > P(X < 4)P(X ≤ 4) = P(X < 4)    P(X ≤ 4) < P(X < 4)

(c)

Calculate

P(3.5 ≤ X ≤ 4.5).

Calculate

P(4.5 < X).

Answer 1

The probability density function of the random variable X is given below

a) the graph of the pdf is given below

Now we will verify probability under curve is 1

Hence it is proved

b) calculate

Solution::

If we compare with

Here X is continuous random variable so, P(X=4)=0

c) calculate

Solution::

Calculate P(4.5<X)

Solution::

P(4.5<X)=P(X>4.5)