Is it possible to have a Binomial Distribution in the following cases:
i. Mean = 5 and Variance = 2.5
ii. P(X = – 2) = 0.1467
iii. P(X less than or not equal to 1) = 0.18
iv. Three parameters i.e. n, p and q
v. P(X = 1) = 0.35
vi. P(X Greater than or equal to 1) = 1.27
vii. .P(X = 3.5) = 0.19
viii. P(1 less than or not equal to X less than or not equal to 4) = 0.79.
i.
"q=0.5, 0<0.5<1"
It is possible.
ii. "X" must be nonnegative.
It is impossible.
iii.
It is possible.
iv. Three parameters "n, p, q" can define a Binomial Distribution.
It is possible.
v. "P(X=1)=0.35"
It is possible.
vi. "P(X\\ge1)=1.27"
It is impossible.
vii. "P(X=3.5)=0.19"
"X" must be integer.
It is impossible.
viii.
"=1-P(X=1)-P(X=4)=0.79"
It is possible.
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