Question

Find the correlation p(X,Y), where X is the number of heads and Y is the number of tails, if a biased coin is thrown with heads p and tossed n time?

Answer #1

Given X is the number of heads and Y is the number of tails, if a biased coin is thrown with heads p and tossed n times, then it has tails(n-p).

Let us imagine the given information in the form of the following table

Tossing number |
Result |
X |
Y |
XY |
X2 |
Y2 |

1 |
H |
1 |
0 |
0 |
1 |
0 |

2 |
H |
1 |
0 |
0 |
1 |
0 |

. |
. |
. |
. |
. |
. |
. |

. |
. |
. |
. |
. |
. |
. |

p |
H |
1 |
0 |
0 |
1 |
0 |

P+1 |
T |
0 |
1 |
0 |
0 |
1 |

P+2 |
T |
0 |
1 |
0 |
0 |
1 |

. |
. |
0 |
1 |
0 |
0 |
1 |

. |
. |
0 |
1 |
0 |
0 |
1 |

n |
T |
0 |
1 |
0 |
0 |
1 |

Sums |
Sx=p |
Sy=n-p |
Sxy=0 |
Sxx=p |
Syy=n-p |

Now, we calculate N = n Sxy - Sx Sy = n*0 – p(n-p) = – p(n-p)

A= n Sxx - Sx2 = np – p2 = p(n-p)

B= n Syy – Sy2 =n(n- p) –(n- p)2 =(n-p)(n-n+p) = (n-p)p = p(n-p)

D= SQRT(A*B)= SQRT(p(n-p)* p(n-p))= p(n-p)

Therefore, the correlation

p(X,Y) = N/D = – p(n-p)/ p(n-p) = – 1.

A coin is tossed five times. Let X = the number of heads. Find
P(X = 3).

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.

A coin with P[Heads]= p and P[Tails]= 1p is tossed repeatedly
(the tosses are independent). Deﬁne (X = number of the toss on
which the ﬁrst H appears, Y = number of the toss on which the
second H appears. Clearly 1X<Y. (i) Are X and Y independent?
Why or why not? (ii) What is the probability distribution of X?
(iii) Find the probability distribution of Y . (iv) Let Z = Y X.
Find the joint probability mass function

A coin with P[Heads]= p and P[Tails]= 1p is tossed repeatedly
(the tosses are independent). Deﬁne (X = number of the toss on
which the ﬁrst H appears, Y = number of the toss on which the
second H appears. Clearly 1X<Y. (i) Are X and Y independent?
Why or why not? (ii) What is the probability distribution of X?
(iii) Find the probability distribution of Y . (iv) Let Z = Y X.
Find the joint probability mass function

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 X and Y be
the random variables that count the number of heads and the number
of tails that come up when three fair coins are tossed. Determine
whether X and Y are independent

Draw the distribution of a random variable X, where X is the
number of heads in a sequence of 10 flips of a weighted coin that
prefers heads twice as much as tails

A coin is tossed with P(Heads) = p
a) What is the expected number of tosses required to get n
heads?
b) Determine the variance of the number of tosses needed to get
the first head.
c) Determine the variance of the number of tosses needed to get
n heads.

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).

A coin is biased so that the probability of the coin landing
heads is 2/3. This coin is tossed three times. A) Find the
probability that it lands on heads all three times. B) Use answer
from part (A) to help find the probability that it lands on tails
at least once.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 14 minutes ago

asked 22 minutes ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago