Random observations from the probability distribution

Reference no: EM131104502

You need to generate 10 random observations from the probability distribution

(a) Prepare to do this by generating 16 random integer numbers from the mixed congruential generator, x_n+1 ≡ (5x_n + 3) (modulo 16) and x₀ = 1.

(b) Use the single-digit random integer numbers from part (a) to generate the desired random observations.

(c) Note that once a particular value of X is generated in part (b), it can never be repeated because each of the 16 possible random integer numbers is generated exactly once in part (a). In which ways does this violate the desirable properties of random observations? What change would you make in what was done in parts (a) and (b) to alleviate this problem?

(d) Now convert the first 10 random integer numbers from part (a) to (approximate) uniform random numbers, and then apply the inverse transformation method to obtain the desired random observations.

(e) Does the procedure prescribed in part (d) actually give a probability of 1/10 of generating each of the 10 possible values of X each time? Explain. What change would you make in what was done in parts (a) and (d) to alleviate this problem?

Reference no: EM131104502

Questions Cloud

Video case-greater chicago food depository : Forty millions pounds of food is disposed annually through the 600-member nonprofit agencies. What are the 600-member nonprofit agencies called in the supply chain?

Consider the discrete random variable : Consider the discrete random variable X that is uniformly distributed (equal probabilities) on the set {1, 2, . . . , 9}. You wish to generate a series of random observations xi (i = 1, 2, . . .) of X.

Calculate the expected return from dell : Calculate the expected return from Dell. Find the highest expected return that is offered by one of these stocks. Find the lowest expected return that is offered by one of these stocks.

Midpoint method-what is the price elasticity of demand : The data in the table above give two points on the demand curve for pizza. Using the midpoint method when the price of a pizza falls from $10 to $9, what is the price elasticity of demand? 0.5, 0.6, 0.9. 2.1. 8.6 The values on the table: Price for pi..

Random observations from the probability distribution : (a) Prepare to do this by generating 16 random integer numbers from the mixed congruential generator, xn+1 ≡ (5xn + 3) (modulo 16) and x0 = 1.

Question regarding the elasticity of supply : Suppose an economist stated that "food stamps serve only to drive food prices higher, not increase the quantity of food available to the poor." For this statement to be true, identify what the elasticity of supply would have to be and explain why.

Generate one random observation from an erlang distribution : Obtaining uniform random numbers as instructed at the beginning of the Problems section, generate four random observations from an exponential distribution with mean = 1.

Illustrating the macro-economic : Assess the external competitive context for an organisation, describing and illustrating the macro-economic, industry or market, competitive environment, key success factors, opportunities and threats for the organisation by completing the followi..

Discuss the appropriate treatment in the financial statement : An amount of $113,000 realized in excess of the cash surrender value of an insurance policy on the life of one of the founders of the company who died during the year.

User Account

All Pages