062/21

10.

Let ‏بوكلا‎ Xo, - - - › ‏رملا - - - بولا بولا کا‎ 06 independent and identically distributed N(u, 62) random

(೫-9)
has a t-distribution with

⋅ −↿⊓ −⋯
∨⊟∏⊟⊔∣≘⊖⋅∟≘↿⋊−≓≓∑⋊↴⊟⊓↺⋏−≓ 1 2۷
0 min

m + 0 - 2 degrees of freedom, then the value of Kis

) mn B) (7401-2) 7
(m+n) (m+n-—2) ಜಗ

Simm

ட D)
(+ क +n-—2)mn J(m+n)(m+n—2) -2(

‎Let 6, and 65 be characteristic functions of two independent random variables X and ۷, which of the‏ ۔

‎following is a characteristic function ?
9
$2

‎A) 04 +% 8) ५1९ ௦) ह 0)

‎be a distribution function which is continuous. Consider two sets of distribution functions‏ ۲۷ء ‎Let F(x), x‏ ۔

‎{F,, ೧21) and {G,, n= 1}, where എ = F(x +n), ഹോ = F(x + (1 )൬. Then which of the following
statements is/are true ?

‎1. F,,(x) converges to a distribution function.

‎2. 500 converges but not to a distribution function.

‎3. நே) converges to a distribution function.

‎4. 09 converges but not to a distribution function.

‎A) 18063 8) 18೧64. 6) 1 only D) 2 only

‎~ Let (|, Xp, . - - be a sequence of independent and identically distributed U(0, 1) random variables.

‎ಗ
‎Let ‏إلا‎ = -2 log (1-26) and Z, = 159 നം distribution of 3027 2) converges to ۸)۸, 1) as
na K

‎o, then a possible value of Kis‏ >- م
‎A) 1 B) 1⁄2 ©) 2 0) २2‏

‎~ For detecting Covid-19 a certain test gives correct diagnosis with probability 0.98. It is known that

‎2% of the population suffers from the disease. If a randomly selected individual from this population
tests positive, then the probability that the selected individual actually has the disease is
A) 0.5 B) 0.2 C) 0.1 D) 06

‎Let 261, Xo, . . - 06 a sequence of independent and identically distributed random variables such that
2 ⋅ ↿⊓ ig ⋅ ⋅
∣⊃≻≺∶↻∶≓∶↿≓⊨≻≺∶↿⋅⊏⊐≘∥⊓≘⋃∶≓⋊⊟⊓↺∨−≓≓ ↿≓⋜⋅⊤⊦∣≘⊓↜⇃⊦∣∣∁⊦∣∘∥⊦∣≘↿∘∣∣∘↜⇃∣⊓

‎⇂↿↿∺⇂↿↿ 12 ೫. 9

‎statements is true ?

‎A) ‏ونا‎ Sand > B) ८-००५-24
0) Un? % and V, > 24 D) ‏جب ينا‎ 26 ०५ 2