1. A jar has two kinds of coins. Some of them are fair, and some
of them have are biased, in which case P(heads) = 2 .
3 A coin is selected from the jar. Since we don’t know which kind
it is, we toss it 50 times. Let X be the number of
heads that occur.
Please note carefully the directions of the inequalities (≤ or ≥)
in each of the questions below.
(a) Suppose the coin chosen is a fair coin. Show how to use a
normal approximation (with continuity correction) to estimate the
probability that X ≥ 29.
(b) Suppose the coin chosen is a biased coin. Show how to use a normal approximation (with continuity correction) to estimate the probability that X ≤ 29.
1. A jar has two kinds of coins. Some of them are fair, and some of them have are biased, in whic...
We toss a fair coin n 400 times and denote Zn the number of heads. (a) What are E(Zn) et Var(Zn)1? (b) What is the probability that Z 200? (use the normal approximation together with the continuity correction (c) What is the smallest integer m such that Pr 200-mくZ.く200 +m] > 20%? (use the normal approximation together with the continuity correction).
We toss a fair coin n 400 times and denote Zn the number of heads. (a) What are E(Zn)...
there are two coins. One is fair and the other one has a 5/8 probability to heads. A coin is chosen at random and tossed twice. Heads shows twice. What is the probability the coin you chose is the biased one
A box contains five coins. For each coin there is a different probability that a head will be obtained when the coin is tossed. (Some of the coins are not fair coins!) Let pi denote the probability of a head when the i th coin is tossed (i = 1, . . . , 5), and suppose that p1 = 0, p2 =1/4, p3 =1/2, p4 =3/4, p5 =1. The experiment we are interested in consists in selecting at random...
We have four fair coins, each of which has probability 1/2 of having a heads outcome and a tails outcome. The experiment is to ip all four coins and observe the sequence of heads and tails. For example, outcome HTHH means coin 1 was heads, coin 2 was tails, coin 3 was heads, coin 4 was heads Note that there are 16 total outcomes, and we assume that each one is equally likely. What is the probability that at there...
6 X Yos have seven coins in youe pocket coins Ceech with probsbility of "heads0.5o Pour two-heaed cons (each with probslity of heade1.0 Suppose you randomily select a coin and g it Find the probablity of lipping "bead Now suppose that you do, in fact, Bip "heads" Givea hat information, find the probabibty that the coin you aipped was: b. A fair con? sA two-headed coin? d. Now suppose that when you flip it, the coin comes up "tails". Given...
- Question 8 a) A green die is biased so that a 6 is 5 times as likely to appear as any other number, and that the five other outcomes are equally likely. Leaving your answer in exact form, what is the probability of a 6 appearing in a single toss of the green die? 5 points 0.5 b) A red die is biased so that the probability that a 1 appears in a single toss is Let X be...
in
the north racial violence
1. (15pts) Consider the following data: 2 4 5 6 8 P(x) 0.1 0.1 0.3 0.2 0.2 0.1 Step 1: The Expected Value E(X) is Round your answer to one decimal. Step 2: The Variance is Round your answer to at least two decimal places. Step 3: The Standard Deviation is Round your answer to at least two decimal places. Step 4: The value of POX>5) is Round your answer to one decimal. Step 5...
1. Suppose that random variables X and Y are independent and have the following properties: E(X) = 5, Var(X) = 2, E(Y ) = −2, E(Y 2) = 7. Compute the following. (a) E(X + Y ). (b) Var(2X − 3Y ) (c) E(X2 + 5) (d) The standard deviation of Y . 2. Consider the following data set: �x = {90, 88, 93, 87, 85, 95, 92} (a) Compute x¯. (b) Compute the standard deviation of this set. 3....
Concept Check: Terminology
0/3 points (graded)
Suppose you observe iid samples X1,…,Xn∼P from some
unknown distribution P. Let F denote a parametric
family of probability distributions (for example, F could be the
family of normal distributions {N(μ,σ2)}μ∈R,σ2>0).
In the topic of goodness of fit testing, our
goal is to answer the question "Does P
belong to the family F, or is P
any distribution outside of F
?"
Parametric hypothesis testing is a particular case of goodness
of fit testing...
Write solutions legibly, and show all work. Walk the reader through your thought process, using English words when necessary. 1. Recall question 2 of the previous homework – We draw 6 cards from a 52 card deck and let X = the number of heart cards drawn. You already found the pmf back then. You’re allowed to use it here without re-deriving it. a. What is the expected value of X? b. What is the variance of X? What is...