Electronics and Communication Engineering - Signals and Systems

46.
If f(t) = - f(- t) satisfies Drichlet conditions, then f(t) can be expanded in Fourier series containing
only sine terms
only cosine terms
cosine terms and constant
sine terms and constant
Answer: Option
Explanation:

Since f( - t) = - f(t) only sine terms will be present because sin (- x) = - sin x.


47.
The joint probability function of two discrete random variable X and Y is given by
x = 0, 2, y = 2, 3 then E(y) is
Answer: Option
Explanation:

.


48.
The joint probability function of two discrete random variable X and Y is given by
x = 0, 2, y = 2, 3 variance σ2 will be
[Hint: σ2 = E(X2) - μ2 ⇒ E(X2) - (E(X))2]
zero
Answer: Option
Explanation:

.


49.
A probability density function is given by p(x) = Ke-x2/2 for -∞ < x < ∞ , The value of K should be
Answer: Option
Explanation:

K can be found by integrating and equating the area under the curve equal to 1.


50.
The Laplace transform of f(t) is
none of the above
Answer: Option
Explanation:

£f(t) =

£-1F(s) = f(t)

£[a f1(t) + bf2(t)] = aF1(s) + bF2(s)

where

£[f(t - T)] = e-sT F(s)

£[e-at f(t)] = F(s + a)

Initial value theorem

Final value theroem

Convolution Integral

where t is dummy variable for t.