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
Answers
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
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: