Question

Write code that when you are given the range and probability distribution of a random variable X. (i.e X ="the number of heads showing on 2 flipped fair coins":

range = (0,1,2)

probability distribution: [.25, .5, .25]

Such that the code returns the expected value, standard deviation, and variance of the random variable . thanks!

Answer 1

Solution :

expected value = $\sum$ X * P(X)

= 0 *0.25 + 1 * 0.5 + 2 *0.25  

= ( 0+ 0.5 + 0.5 )

= 1

Standard deviation = $\sigma$

==$\sqrt$$\sum$X ² * P(X) - $\mu$ ²

=  $\sqrt$[ 0²   * 0.25+ 1²   *0.5 + 2² *0.25 ] - (1)²

= $\sqrt$ [( + 0+ 0.5+ 1) - 1]

= $\sqrt$ 1.5 - 1

=$\sqrt$0.5 =0.7071

variance =$\sum$X ² * P(X) - $\mu$ ²

=[ 0²   * 0.25+ 1²   *0.5 + 2² *0.25 ] - (1)²

=  [( + 0+ 0.5+ 1) - 1]

= 1.5 - 1

=0.5