Continuous Probability Distribution Question

Question

The probability density of a random variable X is given in the figure below.

From this density, the probability that X > 1.18 or X < 0.34 is: ___________

Answer 1

Hi Chrislyn,

Remember the formula for area of a rectangle:

a=lw

Area under a uniform probability distribution is always 1, and we have the length 2 from the x-axis, so:

1=2w

w=1/2

Now, to get the probability that x exceeds 1.18, note that the length is 0.72 and probability is an area. Width remains constant, so

l=0.72

w=1/2

A=P=lw=0.72(1/2)

A=P(X>1.18)=0.36

Now, we do the same procedure for x<0.34.

0.34 is a length, width is still constant, so:

A=(0.34)(1/2)

A=P(X<0.34)=0.17

Now, we simply add the probabilities together:

P(X>1.18 or X<0.34)=(0.36+0.17)

P=0.53

I hope this helps.