Without use the ‘sample’ function, generate a random vector that follows a multi

Question

Without use the ‘sample’ function, generate a random vector that follows a multinomial distribution with probability (0.2, 0.3, 0.5). Hint: Using “runif” or “rbinom”. Please write several lines of R scripts to simulate a multinomial distribution with probability (0.2, 0.3, 0.5).

Calculate the probability for each of the following events: (a) a normally distributed variable with mean 36 and standard deviation 6 is larger than 43 (b) X>6.7 in a chi-square distribution with 3 degrees of freedom (c) getting 10 out of 10 successes in a binomial distribution with probability 0.8

Explanation / Answer

a)
mean = 36, sd = 6
x = 43
P(X > 43) = P(z > (43 - 36)/6)
= P(z > 1.1667)
= 0.1217 (use right tailed z-table to find the area above z=1.1667)

Ans: 0.1217

b)
P(X2 > 6.7) = 0.0821
Excel function used for this =CHISQ.DIST.RT(6.7,3)

c)
P(X = 10) = 0.8^10 = 0.1074

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