Question

let X denote the number of colleges where you will apply after results and probability P(X=x) denotes your chances of getting admission in 'x' colleges. It is given that P(X=x)={kx if x=0 or 1
2kx if x=2
k(5-x) if x=3 or 4;k0
1. find k?
2.find the probability of getting admission in exactly 2 colleges
3. find mean and variance of probability distribution

Answer 1

Answer:

1) 1/8

2)1/2

3)μ = 19/8  ,  σ² = 115.434875

Step-by-step explanation:

Hi,

Let 'X' be the random variable denoting the number of admissions the student had got.

Given tvalues of P(X=x) for different values of x,

from calculations it is clear that P(X=0) = P(X=5) = 0

=> X can take the values 1,2,3 or 4.

Let us prepare a probability distribution table for the random variable 'X'

X=xi             1              2             3             4            

P(X=xi)          K            4K           2K           K      

Also , we know that sum of all the probabilities in a probability distribution is equal to 1      

=> K + 4K + 2k + k = 1

=> 8K = 1

=> K = 1/8.

2) Probability of getting admission in exactly 2 colleges is given by

P(X = 2) = 4K = 1/2

3)  Mean of random variable 'X' is given by ∑x,P(X=xi)

= 1*K + 2*4K +3*2K + 4*K

=19K

μ=19/8

Variance of probability distribution is given by

σ² = ∑(xi - μ)²P(X=xi)

= ∑xi²P(X=xi) - μ²

=1²*k + 2²*4k + 3²*2k + 4²*k - (19/8)²

=51k - 361/64

=51*19/8 - 361/64

=115.484375.

Hope, it helped !