The function 𝑝(𝑥) is given by 𝑝(𝑥) = 𝐴/𝑥𝜇 where 𝐴 and 𝜇 are constants with 𝜇 > 1 and 1 ≤ 𝑥 < ∞ and 𝑝(𝑥) = 0 for −∞ < 𝑥 < 1

August 29, 2023

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Q. The function 𝑝(𝑥) is given by 𝑝(𝑥) = 𝐴/𝑥^𝜇 where 𝐴 and 𝜇 are constants with 𝜇 > 1 and 1 ≤ 𝑥 < ∞ and 𝑝(𝑥) = 0 for −∞ < 𝑥 < 1. For 𝑝(𝑥) to be a probability density function, the value of 𝐴 should be equal to

Sol:

The function 𝑝(𝑥) is given by 𝑝(𝑥) = 𝐴/𝑥𝜇 where 𝐴 and 𝜇 are constants with 𝜇 > 1 and 1 ≤ 𝑥 < ∞ and 𝑝(𝑥) = 0 for −∞ < 𝑥 < 1

The curve y = f (x) is such that the tangent to the curve at every point (𝑥, 𝑦) has a 𝑌-axis intercept 𝑐, given by 𝑐 = −𝑦. Then, f (x) is proportional to

A complex function 𝑓(𝑧) = 𝑢(𝑥, 𝑦) + 𝑖 𝑣(𝑥, 𝑦) and its complex conjugate 𝑓∗(𝑧) = 𝑢(𝑥, 𝑦) − 𝑖 𝑣(𝑥, 𝑦) are both analytic in the entire complex plane

A glass fibre of 5 micron diameter is subjected to a tensile stress of 20 MPa

Determine the correctness (or otherwise) of the following Assertion [A] and the Reason [R]

Determine the correctness (or otherwise) of the following Assertion [A] and the Reason [R]

A copper-aluminium diffusion couple develops a certain concentration profile after an isothermal

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