Math Answers

Four coins are tossed. Let Z be the random variable representing the number of heads that occur. Find the values of the random variable Z.

In (𝑍, +) , let 𝐻 = 𝑠𝑒𝑡 𝑜𝑓 𝑎𝑙𝑙 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑒𝑠 𝑜𝑓 3 and

𝐾 = 𝑠𝑒𝑡 𝑜𝑓 𝑎𝑙𝑙 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑒𝑠 𝑜𝑓 5.

Show that H and K are subgroups of Z . Also describe 𝐻 ∩ 𝐾

Prove the limit of 𝑥𝑛 =1/2 [𝑥𝑛−1 + 𝑥𝑛]

How many circular permutations are there given the numbers on the clock?

Two coins are tossed. Let T be the number of tails that occur.

Construct the probability histogram.

A population consist of the value ( 1,4,3,2). Consider sample of sizes 2 that can be drawn from this population.

Find the distinct interval of length 1 containing a root or solutin of f(x) = x³ - 3x + 5 using IVT

Let p and q be the propositions “You can take the flight” and “You buy a ticket,” respectively.

Express each of these compound propositions as an English sentence.

a) ¬p b) p∨q

c) ¬p∧q d) q → p e) ¬q →¬p

f) ¬p →¬ q g) p ↔ q h) ¬q ∨(¬p∧ q)

Let x be a binomial random variable with n=20 and p = 0.1.

a. Find the formula for the probability distribution of x.

b. Calculate P(X≤4)

c. Calculate the mean and standard deviation of X.

Find the t-value that bound in the middle of 80% with sample size 12