Question

Please solve the following showing all the steps.

Using the sample mean, variance, and standard deviation equations
with steps. I don't know how to do this and would like to
learn.

Also, is this considered a loaded dice?

Consider the roll of two dice. Let X be a random variable representing the sum of the number of dots appearing on each of the dice. The probabilities of each possible value of X are as follows:

2 | 1/36 |

3 | 2/36 |

4 | 3/36 |

5 | 4/36 |

6 | 5/36 |

7 | 6/36 |

8 | 5/36 |

9 | 4/36 |

10 | 3/36 |

11 | 2/36 |

12 | 1/36 |

Determine the expected value and standard deviation of X.

Answer #1

Sol:

Expected value of X

=2*(1/36)+3*(2/36)+4*(3/36)+5*(4/36)+6*(5/36)+7*(6/36)+8*(5/36)+9*(4/36)+10*(3/36)+11*(2/36)+12*(1/36)

E(X)=7

expected value=7

Variance of X=

=2^2*(1/36)+3^2*(2/36)+4^2*(3/36)+5^2*(4/36)+6^2*(5/36)+7^2*(6/36)+8^2*(5/36)+9^2*(4/36)+10^2*(3/36)+11^2*(2/36)+12^2*(1/36)-(7)^2

=54.83333-49

= 5.83333

standard deviation of x=sqrt(variance)=sqrt(5.83333)= 2.415229

ANSWER;

expected value=7

standard deviation of X.=2.415229

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