1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
11111nata11111 [884]
3 years ago
15

If a fair coin is tossed 4 times, there are 16 possible sequences of heads (H) and tails (T). Supposethe random variable X repre

sents the number of heads in a sequence. Construct the probabilitydistribution for X.
Mathematics
1 answer:
postnew [5]3 years ago
8 0

Answer:

The probability distribution of X is:

P(x=0)=0.0625\\\\P(x=1)=0.25\\\\P(x=2)=0.375\\\\P(x=3)=0.25\\\\P(x=4)=0.0625\\\\

Step-by-step explanation:

"Tossing a coin and getting H" can be modelled as a Bernoulli random variable. The variable X is a sum of 4 of this Bernoulli variables, we can model X as a binomial random variable, with p=0.5 and n=4.

The values X can take are: 0, 1, 2, 3 and 4.

The values of this probability are calculated as:

P(x=0) = \binom{4}{0} p^{0}q^{4}=1*1*0.0625=0.0625\\\\P(x=1) = \binom{4}{1} p^{1}q^{3}=4*0.5*0.125=0.25\\\\P(x=2) = \binom{4}{2} p^{2}q^{2}=6*0.25*0.25=0.375\\\\P(x=3) = \binom{4}{3} p^{3}q^{1}=4*0.125*0.5=0.25\\\\P(x=4) = \binom{4}{4} p^{4}q^{0}=1*0.0625*1=0.0625\\\\

Where

p: is the probability of tossing a coin and getting a Heads

q: is the probability of tossing a coin and not getting a Heads.

The binomial number is a way to calculate the possible combinations of getting a certain amount of heads.

For example, in 4 tosses, there are 6 ways or combinations of getting 2 heads and 2 tails:

\binom{4}{2}=\frac{4!}{2!(4-2)!}=\frac{24}{2*2}=6

You might be interested in
Quick math, please help!! Thank you!
SVEN [57.7K]

Answer:

x=32

Step-by-step explanation:

Since we know all the angels are equal to 60, you can pick whichever angel you wish and set it equal to 60 to find the value of x

8 0
3 years ago
Simplify 4 over quantity 2 plus 7 i.
spayn [35]
To simplify 4/(2+7i), we multiply it by a fraction equal to one that removes the i value in the denominator.  The best value to do this is the complex conjugate divided by itself, so we have 4(2-7i)/((2+7i)(2-7i)).  Simplifying, we have (8-28i)/(4-(-49))=(8-28i)/53, which is a completely simplified fraction since 8 and 53 are relatively prime (or coprime), and there are no radicals in the denominator.
3 0
3 years ago
Read 2 more answers
Pls help asap MIDSEGMENTS
kenny6666 [7]

Answer:

Angle 2 = 64°

Step-by-step explanation:

Angle 2 = 180°-116° (int angles, 12//34)

=64°

4 0
3 years ago
1 / f = 1 / a + 1 / b
Sphinxa [80]

That equation can represent the relationship among the image distance,
object distance, and focal length of a lens. 

It could describe the effective resistance of two resistors in parallel, the
effective inductance of two coils in parallel, or the effective capacitance
of two capacitors in series. 

Thanks for sharing it.  Now, did you have a question to ask ?

6 0
3 years ago
Pls help!!!!!!!!!!!!!!!!!
vazorg [7]

Answer:

19 for each one

Step-by-step explanation:

Divide 57 by 3

3 0
3 years ago
Read 2 more answers
Other questions:
  • (9x) (4x^3) (2x^4y) =
    13·1 answer
  • A community bike ride offers a short 5.7 mile ride for children and families the short ride is followed by a long ride 52 over t
    9·1 answer
  • Which is larger 25% or 0.3
    13·2 answers
  • Systems of Equations... <br><br>y = 3x+1<br>y=x+5​
    11·1 answer
  • Write this number in standard form 12 ten thousands, 8 thousands, 14 hundreds, 7 ones
    12·2 answers
  • What happens to a line when the y-intercept is changed? Check all that apply. A. As the y-intercept increases, the graph of the
    8·2 answers
  • If LMN=XYZ, which congruences are true by CPCTC? Check all that apply
    12·2 answers
  • Question number five
    11·1 answer
  • Your friend finds the area of a circle with a diameter of 9 inches. Is your friend correct? Explain
    8·1 answer
  • What is 2.3g as a percentage of 5.98g ? (Round the nearest whole number)
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!