Let x and y be independent random variables with binomial distribution B(10, 1 /3) and B(20, 1/3) respectively. E[x + y]isa)5b)10c)15d)30Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Understanding the Random Variables
Let x and y be independent random variables defined as follows:
- x ~ B(10, 1/3): This means x follows a binomial distribution with 10 trials and a probability of success of 1/3.
- y ~ B(20, 1/3): This means y follows a binomial distribution with 20 trials and a probability of success of 1/3.
Calculating Expected Values
To find E[x + y], we can utilize the property of expectation:
- E[x + y] = E[x] + E[y]
Now, we need to compute E[x] and E[y] individually.
Expected Value of x
For a binomial distribution B(n, p), the expected value is given by:
- E[x] = n * p
So for x:
- E[x] = 10 * (1/3) = 10/3 ≈ 3.33
Expected Value of y
Similarly, for y:
- E[y] = 20 * (1/3) = 20/3 ≈ 6.67
Combining the Expected Values
Now we can combine the expected values:
- E[x + y] = E[x] + E[y]
- E[x + y] = (10/3) + (20/3) = 30/3 = 10
Conclusion
Thus, the expected value of the sum of the two independent random variables x and y is:
- E[x + y] = 10
The correct answer is option b) 10.

Answer

E (x + y) = E (x) + E(y)

Expectation of binomial distribution is np if B(n, p) is the binomial distribution.

Similar Mathematics Doubts

Let X and V be binomial random variables with parameters(n1, p1) and {n2, p2) respectively, where 0 < p1, p2 < 1, p1≠ p2.consider the following statements :P : If E(X)=Var(Y)thenVar(X) < E(Y)Q : If E(X) =E(Y) then Var (X) = Var(Y)Which one of the following is TRUE?

Let X and Y be independent Poisson random variables with parameters 5 and μ, respectively. IfP(XY= 1) = P(X+ Y= 1),then Var(Y) is

Let X be a binomial random variable with parameters n and p. If the mean and thestandard deviation of X are 3 and 3/2,respectively, then what is the value of (n, p)?

X1,X2, .... Xn are independent observations on the random variable X with distribution function F(x). Then the distribution function of Y = Max (X1, X2, ..., Xn) is

If X1and X2 are independent normal random variables with parameters respectively then X1 - X2is normal with meanμand varianceσ2such that

Top Courses for Mathematics

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams