Shankar really likes playing Badminton. On a particular day at Fetzer gym he plays two games (whose outcomes are independent of each other). He has .3 probability of winning the first game and he has .9 probability of winning the second game. There are no ties and as stated above the outcomes of each game are independent of each other. Let X denote the number of games shankar wins.

Calculate E[X] and E[X2].

E[X] = 1.2

E[X2] = 1.74

Step-by-step explanation:

If X is the number of games shankar wins, the sample space for X is [0,1,2], as he can win none, on or the two games.

Let:

Pw1: probability of winning the first game

Pw2: probability of winning the second game

The probability of winning none of the games (X=0) is:

The probability of winning only one of the games (X=1) is:

The probability of winning both games (X=2) is:

The expected value E(X) is:

The expected value of the square of X, E(X^2) can be calculated as:

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.