JEE Main 2020 — Statistics Question with Solution
From: JEE Main 2020 (Online) 2nd September Morning Slot
Question
Let X = {x
N : 1
x
17} and
Y = {ax + b: x X and a, b R, a > 0}. If mean
and variance of elements of Y are 17 and 216
respectively then a + b is equal to :
Y = {ax + b: x X and a, b R, a > 0}. If mean
and variance of elements of Y are 17 and 216
respectively then a + b is equal to :
Choose an option
Show full solutionCorrect option: C
Correct answer
C-7
Step-by-step explanation
Mean of X = = = 9
Mean of Y = = 17
= 17
9a + b = 17 ....(1)
Given Var(Y) = 216
= 216
= 8585
(a + b)2 + (2a + b)2 +....+ (17a + b)2 = 8585
105a2 + b2 + 18ab = 505 ....(2)
From equation (1) & (2)
a = 3 & b = -10
a + b = –7
Mean of Y = = 17
= 17
9a + b = 17 ....(1)
Given Var(Y) = 216
= 216
= 8585
(a + b)2 + (2a + b)2 +....+ (17a + b)2 = 8585
105a2 + b2 + 18ab = 505 ....(2)
From equation (1) & (2)
a = 3 & b = -10
a + b = –7
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