Question

An unfair coin is such that on any given toss, the probability
of getting heads is 0.6 and the probability of getting tails is
0.4. The coin is tossed 8 times. Let the random variable X be the
number of times heads is tossed.

1. Find P(X=5).

2. Find P(X≥3).

3. What is the expected value for this random variable?

E(X) =

4. What is the standard deviation for this random variable? (Give
your answer to 3 decimal places)

SD(X) =

Answer #1

X : the number of times heads is tossed.

X ~ bin (n,p)

where, n = 8 ,p =0.6, q=0.4

the pmf of the distribution be:-

c). **the expected
value for this random variable is:-**

d).**the
standard deviation for this random variable
is:-**

*** if you have any doubt regarding the problem please write it
in the comment box.if you are satisfied please give me a
**LIKE** if possible...

Suppose you toss an unfair coin 8 times independently. The
probability of getting heads is 0.3. Denote the outcome to be 1 if
you get heads and 0 if you get tails.
1.Write down the sample space.
2. What is the probability of the event that you get a head or a
tail at least once?
3. If you get 8 same toss you will get x dollars, otherwise you
will lose one dollar. On average, how large should x...

Suppose you are flipping an unfair coin 10 times. Let p be the
probability of getting tails for said coin. Define X to be the
number of heads obtained.
(a.) Describe the sample space S.
(b.) Give the values x for X.
(c.) Find the likelihood of rolling exactly four heads.
(d.) Find fX(x) .

A weighted coin has probability 0.7 of getting heads, and 0.3 of
getting a tails. If the coin is tossed 6 times, what is the
probability of getting at least 4 heads? What is the probability of
getting less than 4 heads?

Toss an unfair coin with probability of tails as 0.4 for 15
times. What is the probability that tails shows up more than 2
times but less than 6 times?
Group of answer choices
0.398
0.624
0.605
0.376

Consider two coins, one fair and one unfair. The probability of
getting heads on a given flip of the unfair coin is 0.10. You are
given one of these coins and will gather information about your
coin by flipping it. Based on your flip results, you will infer
which of the coins you were given. At the end of the question,
which coin you were given will be revealed.
When you flip your coin, your result is based on a...

You select a coin at random: 2/3 of the coins are unfair, 1/3 of
the coins are fair. The fair coins are equally likely to flip heads
or tails. The unfair coins flip heads 3/4 of the times, and tails
1/4 of the times. You flip the selected coin and get heads or
tails. Find (1) the probability that the selected coin is fair
given the flip is heads, (2) the probability that the selected coin
is fair given the...

Simulates 2 coin toss and calculate emperical probability of
getting double heads.
# Function tossl() simulates coin toss
toss <- function(x) floor(2*runif(x))
# Let c1 tosses from coin 1 and c2 represent tosses of coin 2.
We’ll store 1000 coin tosses in c1 and c2
c1=toss(1000)
c2=toss(1000)
dheads=sum((c1+c2)==2)
# Double heads dheads will occurs when corresponding sum of
outcomes is 2
# == operator is TRUE only when the sum of corresponding tosses is
2 (Two
heads came up)
#sum((c1+c2)==2)...

You flip a coin until getting heads. Let X be the number of coin
flips.
a. What is the probability that you flip the coin at least 8
times?
b. What is the probability that you flip the coin at least 8
times given that the first, third, and fifth flips were all
tails?
c. You flip three coins. Let X be the total number of heads. You
then roll X standard dice. Let Y be the sum of those...

Q3. Suppose you toss n “fair” coins (i.e.,
heads probability = 1/21/2). For every coin that came up tails,
suppose you toss it one more time. Let X be the random variable
denoting the number of heads in the end.
What is the range of the variable X (give exact upper and lower
bounds)
What is the distribution of X? (Write down the name and give a
convincing explanation.)

A weighted coin has a probability of 0.6 of getting a head and
0.4 of getting a tail.
(a) In a series of 30 independent tosses what is the probability
of getting the same number of heads as tails? [2]
(b) Find the probability of getting more than 7 heads in 10
tosses? [3]
(c) Find the probability of 4 consecutive tails followed by 2
tails in the next 6 tosses. [2]

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