If random variable X counts the number of coin flips to get a Tail, then it has the following PDF
x | 1 | 2 | 3 | 4 | ... | k |
f ( x ) | 2/3 | 2/9 | 2/27 | 2/81 | ... | 2/3^k |
What is P ( x ≥ 4 )
Answer choices:
8/27
2/27
26/27
None of these
1/27
If random variable X counts the number of coin flips to get a Tail, then it...
The PMF of the experiment that records the number of heads in four flips of a coin, which can be obtained with the R commands attach (expand.grid (X1=0:1, X2=0:1, X3=0:1, X4=0:1)); table(X1+X2+X3+X4)/length(X1), is x 0 1 2 3 4 p(x) 0.0625 0.25 0.375 0.25 0.0625 Thus, if the random variable X denotes the number of heads in four flips of a coin then the probability of, for example, two heads is P(X = 2) = p(2) = 0.375. What is...
A coin is tossed twice. Let
the random variable X denote the number of tails that occur in the
two tosses. Find the P(X ≤ 1)
Question 2: A coin is tossed twice. Let the random variable X denote the number of tails that occur in the two tosses. Find the P(Xs 1) a. 0.250 b. 0.500 c. 0.750 d. 1.000 e. None of the above
One gambler flips a fair coin in three separate times. Letting a random variable X represent his winnings in the following way: He loses $1 if he gets no heads in three flips; he wins $1, $2, and $3 if he obtains 1, 2, or 3 heads, respectively. (a) Find the probability mass function of X. (b) Find the probability density function of X. (c) Find the cumulative distribution function of X. (d) Find the probability that he wins more...
Recall the Geometric(p) distribution where X = number of flips of a coin until you get a head (H) with Pr(H) = p. The distribution is Pr(X = x) = (1 − p) (x−1) p for x = 1, 2, . . . , with mean E(X) = ∑ x=1∞ (x(1 − p) (x−1) p) = 1/p, which can be obtained by brute force. An easier way to find the mean is to condition on the first toss, say Y...
The PMF of the experiment that records the number of heads in four flips of a coin, which can be obtained with the R commands attach (expand.grid (X1=0:1, X2=0:1, X3=0:1, X4=0:1)); table(X1+X2+X3+X4)/length(X1), is x 0 1 2 3 4 p(x) 0.0625 0.25 0.375 0.25 0.0625 Thus, if the random variable X denotes the number of heads in four flips of a coin then the probability of, for example, two heads is P(X = 2) = p(2) = 0.375. What is...
A fair coin is flipped independently until the first Heads is observed. Let the random variable K be the number of tosses until the first Heads is observed plus 1. For example, if we see TTTHTH, then K = 5. For k 1, 2, , K, let Xk be a continuous random variable that is uniform over the interval [0, 5]. The Xk are independent of one another and of the coin flips. LetX = Σ i Xo Find the...
Problem 3.
3. For a nonnegative integer-valued random variable X show that i-0 4. A coin comes up heads with probability p. It is flipped until two consecutive heads or two consecutive tails occur. Find the expected number of flips 5. Suppose that PX a)p, P[Xb-p, a b. Show that (X-b)/(a-b) is a Bernoulli variable, and find its variance
3. For a nonnegative integer-valued random variable X show that i-0 4. A coin comes up heads with probability p. It...
A coin will be tossed multiple times. Probability of head is 1/2, and probability of tail is 1/2. they are independent from each other. X is a random variable that counts how often the coin must be tossed until the first head appears. calculate for all k=1,2,3,..., how big the probability is for: i) X=k ii) X>k iii) X<k
Problem 0.2 Recall the Geometric(p) distribution where X-number of flips of a coin until you get a head (H) with Pr(H) -p. The distribution is Pr(X- (1-p)1p for 1,2,. , with mean E(X)x(1 - p)*-p- 1/p, which can be obtained by brute force. An easier way to find the mean is to condition on the first toss, say Y- 0or 1 if the first toss is T or H. Show the mean is 1/p using E(X) EE(X Y)
A coin is tossed three times. X is the random variable for the number of heads occurring. a) Construct the probability distribution for the random variable X, the number of head occurring. b) Find P(x=2). c) Find P(x³1). d) Find the mean and the standard deviation of the probability distribution for the random variable X, the number of heads occurring.