The element titanium has five stable occurring isotopes, differing from each other in the number of neutrons an atom contains. If Xis the number of neutrons in a randomly chosen titanium atom, the probability mass function of X is given as follows:

a. Find μX.

b. Find σX.

Solution 6E

Step1 of 3:

We have the element titanium has five stable occurring isotopes, differing from each other in number of neutrons an atom contains.

Let X is the number of neutrons in a randomly chosen titanium atom, the probability mass function is given as follows:

x | 24 | 25 | 26 | 27 | 28 |

P(x) | 0.0825 | 0.0744 | 0.7372 | 0.0541 | 0.0518 |

We need to find,

a).Find

b).Find

Step2 of 3:

a).

Mean is given by

=

= (1.8) + (1.86) + (19.1672) + (1.4607) + (1.3986)

= 25.6865

Therefore, 25.6865.

Step3 of 3:

b).

Variance of X is given by

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