Question

Let X be the random variable representing the difference between the number of headsand the number...

Let X be the random variable representing the difference between the number of headsand the number of tails obtained when a fair coin is tossed 4 times.

a) What are the possible values of X?

b) Compute all the probability distribution of X?

c) Draw the cumulative distribution function F(x) of the random variable X.

Homework Answers

Answer #1

a)possible values of X are -4,-2,0,2,4.

b) below is  probability distribution of X:

P(X=-4)=P(0 heads and 4 tails)= =1/16

P(X=-2)=P(1 heads and 3 tails)= =4/16=1/4

P(X=0)=P(2 heads and 2 tails)= =6/16=3/8

P(X=2)=P(3 heads and 1 tails)= =4/16=1/4

P(X=4)=P(4 heads and 0 tails)==1/16

c)

from above below is CDF of X:

0        x<-4
   1/16 -4<=x<-2
F(X)=    5/16 for -2<=x<0
11/16 0<=x<2
15/16 2<=x<4
1        x>=4

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A coin is tossed 5 times. Let the random variable ? be the difference between the...
A coin is tossed 5 times. Let the random variable ? be the difference between the number of heads and the number of tails in the 5 tosses of a coin. Assume ?[heads] = ?. Find the range of ?, i.e., ??. Let ? be the number of heads in the 5 tosses, what is the relationship between ? and ?, i.e., express ? as a function of ?? Find the pmf of ?. Find ?[?]. Find VAR[?].
Let X represent the difference between the number of heads and the number of tails when...
Let X represent the difference between the number of heads and the number of tails when a coin is tossed 42 times. Then P(X=12)= ? Please show work with arithmetic.
Let X represent the difference between the number of heads and the number of tails when...
Let X represent the difference between the number of heads and the number of tails when a coin is tossed 48 times. Then P(X=8)= So far I got 0.05946 but it keeps telling me I'm wrong
Let W be a random variable giving the number of heads minus the number of tails...
Let W be a random variable giving the number of heads minus the number of tails in three independent tosses of an unfair coin where p = P(H) = 1 3 , and q = P(T) = 2 3 . (a) List the elements of the sample space S for the three tosses of the coin and to each sample point assign a value of W. (b) Find P(−1 ≤ W < 1). (c) Draw a graph of the probability...
Suppose a coin is tossed three times and let X be a random variable recording the...
Suppose a coin is tossed three times and let X be a random variable recording the number of times heads appears in each set of three tosses. (i) Write down the range of X. (ii) Determine the probability distribution of X. (iii) Determine the cumulative probability distribution of X. (iv) Calculate the expectation and variance of X.
A fair coin has been tossed four times. Let X be the number of heads minus...
A fair coin has been tossed four times. Let X be the number of heads minus the number of tails (out of four tosses). Find the probability mass function of X. Sketch the graph of the probability mass function and the distribution function, Find E[X] and Var(X).
1. A coin is tossed 3 times. Let x be the random discrete variable representing the...
1. A coin is tossed 3 times. Let x be the random discrete variable representing the number of times tails comes up. a) Create a sample space for the event;    b) Create a probability distribution table for the discrete variable x;                 c) Calculate the expected value for x. 2. For the data below, representing a sample of times (in minutes) students spend solving a certain Statistics problem, find P35, range, Q2 and IQR. 3.0, 3.2, 4.6, 5.2 3.2, 3.5...
1. In this problem, a fair coin is flipped three times. Assume that a random variable...
1. In this problem, a fair coin is flipped three times. Assume that a random variable X is defined to be 7 times the number of heads plus 4 times the number of tails. How many different values are possible for the random variable X? 2. Fill in the table below to complete the probability density function. Be certain to list the values of X in ascending order. Value of X | Probability   
In this problem, a fair coin is flipped three times. Assume that a random variable X...
In this problem, a fair coin is flipped three times. Assume that a random variable X is defined to be 7 times the number of heads plus 4 times the number of tails. How many different values are possible for the random variable X?
X is a discrete random variable representing number of conforming parts in a sample and has...
X is a discrete random variable representing number of conforming parts in a sample and has following probability mass function ?(?) = { ?(5 − ?) if ? = 1, 2, 3, 4 0 otherwise i) Find the value of constant ? and justify your answer . ii) ( Determine the cumulative distribution function of X, (in the form of piecewise function). iii) Use the cumulative distribution function found in question 2 to determine the following: a) ?(2 < ?...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT