Find the probability that at least one molecule in the breath you just took was shared with caesar’s last breath, and give a sim
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The question is incomplete. The complete question is :
Let X be a random variable with probability mass function
P(X =1) =1/2, P(X=2)=1/3, P(X=5)=1/6
(a) Find a function g such that E[g(X)]=1/3 ln(2) + 1/6 ln(5). You answer should give at least the values g(k) for all possible values of k of X, but you can also specify g on a larger set if possible.
(b) Let t be some real number. Find a function g such that E[g(X)] =1/2 e^t + 2/3 e^(2t) + 5/6 e^(5t)
Solution :
Given :
a). We know :
So,
Therefore comparing both the sides,
Also,
b).
We known that
∴
Therefore on comparing, we get
∴
Using a system of equations, it is found that Carol is 10 years old.
The complete problem is:
"Gerrys age is 5 more than three times Carols age. If the sum of their age is 45, how old is carol?"
<h3>System</h3>The variables are:
- Variable x: Gerry's age.
- Variable y: Carol's age.
Gerry is <u>5 more than three times Carol's age</u>, hence:
The sum of their ages is 45, hence:
We then use the first equation to find Carol's age:
Carol is 10 years old.
To learn more about system of equations, you can take a look at brainly.com/question/13773803