Q1. Which of the following statements are true or false? Give a short proof or a counter-example in support of your answer.
- (i)) The mean of a binomial distribution, when n = 6 and P(X = 4) = P(X = 2) is 3/2 (80 words)
- (ii)) Mean deviation is minimum about median. (80 words)
- (iii)) The domain of 6x³ −7 y³ + 4xy, where it is continuous is − ∞ < x < ∞, 0 < y < ∞. (80 words)
- (iv)) ∫_1^2 1/x dx = 7/23 (80 words)
- (v)) The CDF of any distribution satisfies F(−∞) = 0, F(∞) =1 and non-decreasing. (80 words)
- Binomial distribution mean: μ = np.
- Mean deviation is minimized about the median.
- Polynomial functions are continuous on their entire domain Rⁿ.
- The integral of 1/x is ln|x|.
Answer: