Probability

1
PROBABILITY AND RANDOM VARIABLES

• B.TECH YEAR II
• SEMESTER III
• 2014-18

2
Standard Normal Distribution

• Here x is a normal function and we can find the
  pdf of x using the formula of Gaussian pdf
  method and after putting the value of µ and s in
  the equation of Gaussian pdf, we can get the
  standard normal value for the new function z.

3
Standard Normal Curve

• This is the standard normal curve, it is spread
  over the region -8 to 8, mean of the standard
  normal function is 0 and area under the curve
  form -8 to 0 and 0 to 8 is equal and there value
  is 0.5 because the curve is symmetric

4
Conversion Method from Normal to Standard normal

• We know that and we have to find
  P(altxltb), so now we can replace the value of x
  with respect to z , which will give us
  
• Now, we will get,

5
Example

• now find the area under the
  standard normal curve when (2x 4) and find its
  expectation.
• here, µ1 and s2
• we have to find
• After this step just
• put the value from 0 to 0.5 and 0 to 1 from
  the standard normal curve, and we will get a
  value, that will be the area under the curve

6
Find the PDF of y

• If , for this case we can conclude that
• and if we want to find the pdf of y,
  the value will be ,

7

• Thank You.....