JAM Mathematical Statistics Question Paper 2019 Download Free PDF
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JAM Mathematical Statistics Question Paper 2019
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Q.1. The lifetime (in years) of bulbs is distributed as an 𝐸𝑥𝑝(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
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 𝑋 and 𝑌 be i.i.d. 𝑈(0, 1) random variables. Then 𝐸(𝑋|𝑋 > 𝑌) equals
Q.4. Let 𝐸 and 𝐹 be any two independent events with 0 < 𝑃(𝐸) < 1 and 0 < 𝑃(𝐹) < 1.
Which one of the following statements is NOT TRUE?
(A) 𝑃(Neither 𝐸 nor 𝐹 occurs) = (𝑃(𝐸) − 1)(𝑃(𝐹) − 1)
(B) 𝑃(Exactly one of 𝐸 and 𝐹 occurs) = 𝑃(𝐸) + 𝑃(𝐹) − 𝑃(𝐸)𝑃(𝐹)
(C) 𝑃(𝐸 occurs but 𝐹 does not occur) = 𝑃(𝐸) − 𝑃(𝐸 ∩ 𝐹)
(D) 𝑃(𝐸 occurs given that 𝐹 does not occur) = 𝑃(𝐸)
Q.5. Let 𝑃 be a 3 × 3 non-null real matrix. If there exist a 3 × 2 real matrix 𝑄 and
a 2 × 3 real matrix 𝑅 such that 𝑃 = 𝑄𝑅, then
(A) 𝑃𝒙 = 𝟎 has a unique solution, where 𝟎 ∈ ℝ3
(B) there exists 𝒃 ∈ ℝ3 such that 𝑃𝒙 = 𝒃 has no solution
(C) there exists a non-zero 𝒃 ∈ ℝ3 such that 𝑃𝒙 = 𝒃 has a unique solution
(D) there exists a non-zero 𝒃 ∈ ℝ3 such that 𝑃 𝑇𝒙 = 𝒃 has a unique solution
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