Binomial Distribution
Question
Q1.
Population S.D is an example of
(a) Parameter (b) Statistic (c) Probability distribution
(d) None of these
Solution.
(a) Parameter
Solution
Q2.
In binomial distribution if p >
1/2
,
then it is _________________ skewed distribution .
(a) Negatively (b) Positively (c) Symmetric
(d) None
(a) Negatively
Solution
Q3.
Maximum variance is 9, find mode of binomial distribution .
Solution.
Maximum variance is
n/4
at p = q = 0.5
n/4
= 9 ⇒
n = 36
mode = (n+1)P = (36 + 1)
1/2
= 18.5(non integer)
So mode is 18(Higher included integer)
Solution
Q4.
If n = 8 and p = 0.4, binomial distribution will be ___________ .
(a) bimodal (b) unimodal (c) None
(d) Can't determine
Solution.
mode = (n+1)P =(9) (0.4) = 3.6
so, mode = 3
binomial distribution unimodal
Solution
Q5.
In Binomial maximum value of variance is 10, find E(x) .
Solution.
As we know that the maximum value of variance is
n/4
at P = 0.5
n/4
= 10 , n = 40
so, E(x) = nP = (40)(0.5) = 20
Solution
Q6.
Probability distribuion may be
(a) Continuous (b) Discrete (c) Both (d) Neither
Solution.
(c) Both
Solution
Q7.
In Binomial distribution n = 10 , p =
1/4
find variance ,
Solution.
= npq = 10 x
1/4
x
3/4
=
30/16
=
15/8
Solution
Q8.
There are two variables x and y (and both are independent variables) having parameters 10,
1/3
and 25,
1/3
respectively. what will be parametres of
(x+y).
Solution.
As per additive property
x &8767; B (n
1,p) and y &8767; B (n
2,p)
(x+y) &8767; B(n
1 +
n
2, p)
So, parameters of (x+y) &8767; (35,
1/3
) .
Solution
Q9.
Statistical measurement of population is known as
Solution.
Parameter
Solution
Q10.
Binomial distribution will be unimodal or bi-modal if n = 7 and P = 1/3
Solution.
= (n + 1)P = 8.(1/3) = 2.67 (non - integer)
So, mode is only 2 (higher included integer)
Binomial distribution is unimodal
Solution
