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## JAM Mathematical Statistics Question Paper 2019

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SAMPLE QUESTIONS

Q.1. The lifetime (in years) of bulbs is distributed as an πΈπ₯π(1) random variable. Using Poisson
approximation to the binomial distribution, the probability (round off to 2 decimal places)
that out of the fifty randomly chosen bulbs at most one fails within one month equals

(A) 0.05

(B) 0.07

(C) 0.09

(D) 0.11

Q.2. In a production line of a factory, each packet contains four items. Past record shows that
20% of the produced items are defective. A quality manager inspects each item in a packet
and approves the packet for shipment if at most one item in the packet is found to be
defective. Then the probability (round off to 2 decimal places) that out of the three
randomly inspected packets at least two are approved for shipment equals __________

Q.3. Let π and π be i.i.d. π(0, 1) random variables. Then πΈ(π|π > π) equals

(A) β

(B) Β½

(C) β

(D) ΒΎ

Q.4. Let πΈ and πΉ be any two independent events with 0 < π(πΈ) < 1 and 0 < π(πΉ) < 1.
Which one of the following statements is NOT TRUE?

(A) π(Neither πΈ nor πΉ occurs) = (π(πΈ) β 1)(π(πΉ) β 1)

(B) π(Exactly one of πΈ and πΉ occurs) = π(πΈ) + π(πΉ) β π(πΈ)π(πΉ)

(C) π(πΈ occurs but πΉ does not occur) = π(πΈ) β π(πΈ β© πΉ)

(D) π(πΈ occurs given that πΉ does not occur) = π(πΈ)

Q.5. Let π be a 3 Γ 3 non-null real matrix. If there exist a 3 Γ 2 real matrix π and
a 2 Γ 3 real matrix π such that π = ππ, then

(A) ππ = π has a unique solution, where π β β3

(B) there exists π β β3 such that ππ = π has no solution

(C) there exists a non-zero π β β3 such that ππ = π has a unique solution

(D) there exists a non-zero π β β3 such that π ππ = π has a unique solution