Lesson test: The binomial distribution

1.[1p]
At what value of $p$ is the variance $p (1 - p)$ of a single Bernoulli trial largest?

CorrectNot quite: 0.5

2.[2p]
Where does the factor $C (n, k)$ in the binomial mass function come from?

It counts the sequences of $n$ trials that contain exactly $k$ successes

Correct

It corrects for the trials not being independent

The answer is: It counts the sequences of $n$ trials that contain exactly $k$ successes

It ensures the probabilities do not exceed one

The answer is: It counts the sequences of $n$ trials that contain exactly $k$ successes

It counts the number of successes

The answer is: It counts the sequences of $n$ trials that contain exactly $k$ successes

3.[2p]
A fair coin is tossed ten times. What is the probability of exactly three heads? Give the answer to four decimal places.

CorrectNot quite: 0.1172

4.[2p]
A machine has a $5$ percent defect rate. What is the probability that a box of $20$ items contains no defects? Give the answer to four decimal places.

CorrectNot quite: 0.3585

6.[3p]
Which assumptions does the binomial formula require?

Select all that apply

The number of trials is fixed before the experiment starts

Correct

The trials are independent

Correct

The success probability is the same on every trial

Correct

The number of successes is fixed before the experiment starts

The answer is: The number of trials is fixed before the experiment starts, The trials are independent, The success probability is the same on every trial

7.[3p]
Weldon threw twelve dice $26306$ times, counting fives and sixes. If $p$ were exactly $1 / 3$ , what would the expected total number of successes be?

CorrectNot quite: 105224

9.[3p]
What does memorylessness mean for a geometric waiting time?

After any number of failures, the remaining wait has the original distribution

Correct

The wait gets shorter the longer you have waited

The answer is: After any number of failures, the remaining wait has the original distribution

The trials become dependent after the first failure

The answer is: After any number of failures, the remaining wait has the original distribution

The expected wait is infinite

The answer is: After any number of failures, the remaining wait has the original distribution

Sign in

The binomial distribution

1.[1p]
At what value of $p$ is the variance $p (1 - p)$ of a single Bernoulli trial largest?

2.[2p]
Where does the factor $C (n, k)$ in the binomial mass function come from?

3.[2p]
A fair coin is tossed ten times. What is the probability of exactly three heads? Give the answer to four decimal places.

4.[2p]
A machine has a $5$ percent defect rate. What is the probability that a box of $20$ items contains no defects? Give the answer to four decimal places.

5.[2p]
For $X \sim Bin (20, 0.05)$ , what is the variance?

6.[3p]
Which assumptions does the binomial formula require?

7.[3p]
Weldon threw twelve dice $26306$ times, counting fives and sixes. If $p$ were exactly $1 / 3$ , what would the expected total number of successes be?

8.[2p]
A fair die is rolled until a six appears. On average, how many rolls does that take?

9.[3p]
What does memorylessness mean for a geometric waiting time?

1.[1p] At what value of p is the variance p(1-p) of a single Bernoulli trial largest?

2.[2p] Where does the factor C(n,k) in the binomial mass function come from?

3.[2p] A fair coin is tossed ten times. What is the probability of exactly three heads? Give the answer to four decimal places.

4.[2p] A machine has a 5 percent defect rate. What is the probability that a box of 20 items contains no defects? Give the answer to four decimal places.

5.[2p] For X∼Bin(20,0.05), what is the variance?

6.[3p] Which assumptions does the binomial formula require?

7.[3p] Weldon threw twelve dice 26306 times, counting fives and sixes. If p were exactly 1/3, what would the expected total number of successes be?

8.[2p] A fair die is rolled until a six appears. On average, how many rolls does that take?

9.[3p] What does memorylessness mean for a geometric waiting time?

1.[1p]
At what value of $p$ is the variance $p (1 - p)$ of a single Bernoulli trial largest?

2.[2p]
Where does the factor $C (n, k)$ in the binomial mass function come from?

3.[2p]
A fair coin is tossed ten times. What is the probability of exactly three heads? Give the answer to four decimal places.

4.[2p]
A machine has a $5$ percent defect rate. What is the probability that a box of $20$ items contains no defects? Give the answer to four decimal places.

5.[2p]
For $X \sim Bin (20, 0.05)$ , what is the variance?

6.[3p]
Which assumptions does the binomial formula require?

7.[3p]
Weldon threw twelve dice $26306$ times, counting fives and sixes. If $p$ were exactly $1 / 3$ , what would the expected total number of successes be?

8.[2p]
A fair die is rolled until a six appears. On average, how many rolls does that take?

9.[3p]
What does memorylessness mean for a geometric waiting time?