Questions asked by minerva

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• Consider the function U defined on R^2, where U(x,y) = sq rt (3x + y). Which of the following statements is true? 1. U is strictly concave 2. U is strictly quasi-concave 3. U is both strictly concave & strictly quasi-concave 4. U is both concave & quasi
  
• What are the inflection points for f(x)= x (6-x) ^ 2/3 ?? 1. 3.6, 6 2. 3.6, 7.2 3. 6, 7.2 4. 3.6
  
• The probability density function of x is given as f(x) = ae^-x/5 for x > 0. The value of a is ? (a) 0·5 (b) 0·3 (c) 0·2 (d) 0·1
  
• If the probability density function of #X# is #f(x) = (1+ax) /2, -1 le x le 1, -1 le a le 1# then the expectation of #X# is? (a) #6/a# (b) #a /3# (c) #a /2# (d) #3/a#
  
• How many real roots does this polynomial have? f (x) = 4x^5 + x^3 + 7x - 2 Options: a) 1 b) 3 c) 4 d) 5
  
• The function f (x) is defined as #f (x) = {(-1, x ≤ 0),( (x + 2) ^ 2, 0 < x ≤ 3),(x, x > 3):}#. The area under the f (x) curve between x = (-2) and x = 5 is? Options: a) 27 b) 205/3 c) 155/3 d) 80
  
• A continuous random variable X has the p.d.f., f (x) = 3x^2; 0 ≤ x ≤ 1. The value of a constant λ that satisfies the relation Pr {X ≤ λ} = Pr {X > λ} is ? a) (1/3)^1/2 b) (1/2)^1/3 c) (2/3)^1/2 d) (2/3)^1/3
  
• Conditional probability using two-way tables?
  
• Find area under the curve? Pl refer to the question in the img attached
  
• Joint probability- mean and variance? Pl refer image attached