Social Sciences, asked by reyrazel2567, 1 day ago

two dice are rolled .let x is a random variable denoting the sum of the numbers on the two dice. find given probability distribution of x

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Answered by krishjatin02
0

The sample space for your experiment is S={(m,n):m,n∈Zand1≤m,n≤6}.

A random variable associated with an experiment is a real-valued function X on the sample space S. Here, X(m,n)=m+n taking values from 2 to 12.

We then say X is a random variable on S, taking values 2,3,4,….,12 and by P(X=k) we mean P(X^{-1}(k)), where X^{-1}(k) contain those (m,n) whose sum is k. (It is generally probability of getting sum k.)

Now we know for a finite sample space P(X=k)=#X^{-1}(k)/#S, from this you will get all the probabilities by counting cardinality of these sets.

(See the picture: from Wikipedia)

The probability distribution of a discrete random variable is generally a function, mapping values of a random variable to their respective probabilities. Defining, f: X → [0,1] such that f(k) = P(X=k). Note: here domain of f is values taken by random variable X.

The formula for expectation is given by,

E(X)= ∑k∈X  k.P(X=k)

=(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)  = 7

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Answered by IqBroly
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Answer:

29-Oct-2021 — two dice are rolled .let x is a random variable denoting the sum of the numbers on the two dice. find given probability distribution of x.

Explanation:

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