Higher Study | Engineering Mathematics

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Probability and Statistics Linear Algebra Graph Theory Set Theory & Algebra Mathematical Logic Calculus Numerical Methods Complex Variables

Questions

Let X and Y be two independent random variables. Which one of the relations between expectation (E), variance (Var) and covariance (Cov) given below is FALSE?

ক

E(XY) = E(X) E(Y)

খ

Cov (X, Y) = 0

গ

Var (X + Y) = Var (X) + Var (Y)

ঘ

E(X<sup>2</sup>Y<sup>2</sup>) = (E(X))<sup>2</sup> (E(Y))<sup>2</sup>

If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?

ক

$$\frac{1}{3}$$

খ

$$\frac{1}{4}$$

গ

$$\frac{1}{2}$$

ঘ

$$\frac{2}{3}$$

Consider a company that assembles computers. The probability of a faulty assembly of any computer is p. The company therefore subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability of q. What is the probability of a computer being declared faulty?

ক

pq + (1 - p) (1 - q)

খ

(1 - q)p

গ

(1 - p)q

ঘ

pq

Which one of the following equations is a correct identity for arbitrary 3 × 3 real matrices P, Q and R?

ক

P(Q + R) = PQ + RP

খ

(P - Q)<sup>2</sup> = P<sup>2</sup> - 2PQ + Q<sup>2</sup>

গ

det (P + Q) = det P + det Q

ঘ

(P + Q)<sup>2</sup> = P<sup>2</sup> + PQ + QP + Q<sup>2</sup>