Stadistics

BUSINESS AND MANAGEMENT SCHOOL MODULE: BUSINESS STATISTICS I Unit 5.- Random variables. Probability distributions.

1. A car factory makes “n” defective cars each day with a probability function: 71 P( x ) =   88

n

n = 0,1,2,3, ,

Calculate: a) The probability of producing no defective car in a day. b) The probability of producing more than a defective car in a day. c) The probability of producing two defective cars in a day.

2. The smartphones sold daily represent a random variable X whose probability distribution is given by: kx x = {0,1,2,...,5} P(x ) =  other case 0 Calculate: a) k b) The distribution function c) The probability that a smartphone is sold in a day d) The probability that more than three smartphones are sold in a day

3. The number of phone calls per day made by a customer is a random variable with this probability function:

  P( x) =   

( )

k 1 3 0

x=0 x>0 other cases

x

Calculate: a) k b) The distribution function c) The probability that a customer makes at least one call, but two at the most

4. The weekly demand (in thousand units) of a certain commodity by a firm is random with the following probability function: k ( x − 1) 2 si 1 < x < 3 , f ( x) =  other cases  0

1

a) b) c) d)

Calculate: k The distribution function The probability that the firm demands more than 2,000 units in a single week Which stock should the firm keep to guarantee that it can satisfy its weekly demand with a probability of 95%?

5. Given the next function:

 kx  f ( x ) = 2 − x  0 

0 < x 1  f ( x) =  x 0 x ≤1  Calculate: a) Check if f(x) is actually a density function. b) The distribution function. c) The probability that the expense is between 1,000 and 3,000 euros. d) The probability that the expense is larger than 10,000 euros.

7. The length of a phone call follows the next probability distribution:

x 0 f ( x) =  x≤0 0 Calculate: a) The average repairing time. b) The most frequent...