Let f(x) be the continuous probability density function of a random variable X. The probability that a < X ≤ b, is
A. $${\text{f}}\left( {{\text{b}} - {\text{a}}} \right)$$
B. $${\text{f}}\left( {\text{b}} \right) - {\text{f}}\left( {\text{a}} \right)$$
C. $$\int\limits_{\text{a}}^{\text{b}} {{\text{f}}\left( {\text{x}} \right){\text{dx}}} $$
D. $$\int\limits_{\text{a}}^{\text{b}} {{\text{xf}}\left( {\text{x}} \right){\text{dx}}} $$
Answer: Option C
This Question Belongs to Engineering Maths >> Probability And Statistics
A coin is tossed 4 times. What is the probability of getting heads exactly 3 times?
A. $$\frac{1}{4}$$
B. $$\frac{3}{8}$$
C. $$\frac{1}{2}$$
D. $$\frac{3}{4}$$
A. 1 and $$\frac{1}{3}$$
B. $$\frac{1}{3}$$ and 1
C. 1 and $$\frac{4}{3}$$
D. $$\frac{1}{3}$$ and $$\frac{4}{3}$$
A. E(XY) = E(X) E(Y)
B. Cov (X, Y) = 0
C. Var (X + Y) = Var (X) + Var (Y)
D. E(X2Y2) = (E(X))2 (E(Y))2
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