Probability distribution, find constant

In summary: Different constants would need to be plugged in in order for the two lists to match up.In summary, Deathfish has apparently misunderstood the problem.
  • #1
Deathfish
86
0

Homework Statement



x = 0, P(x) = 0.4
x = 1, P(x) = 0.1
x = 2, P(x) = 0.1
x = 3, P(x) = 0.1
x = 4, P(x) = 0.3

If P(x)=k(5-x) for x = 0,1,2,3,4, find value of constant k

The Attempt at a Solution



0.4 = k(5-0)
0.1 = k(5-1)
0.1 = k(5-2)
0.1 = k(5-3)
0.3 = k(5-4)

5k+4k+3k+2k+k=1
15k=1
k = 1/15
 
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  • #2
Deathfish said:
If P(x)=k(5-x) for x = 0,1,2,3,4, find value of constant k

Are you sure you have stated the problem correctly? The sum of the probabilities is already 1.
 
  • #3
The probability distribution,
x = 0, P(x) = 0.4
x = 1, P(x) = 0.1
x = 2, P(x) = 0.1
x = 3, P(x) = 0.1
x = 4, P(x) = 0.3

does NOT satisfy P(x)= k(5- x). If it did, then you would have to have P(0)= 0.4= k(5)so that k= 0.4/5= 0.08 but then P(1)= k(5-1)= 0.08(4)= 0.32, not 0.1. If P(x)= k(5- x) then 15k= 1 because any probability distribution must sum to 1, not because of "0.4+ 0.1+ 0.1+ 0.1+ 0.3= 1".
 
  • #4
Deathfish said:

Homework Statement



x = 0, P(x) = 0.4
x = 1, P(x) = 0.1
x = 2, P(x) = 0.1
x = 3, P(x) = 0.1
x = 4, P(x) = 0.3

If P(x)=k(5-x) for x = 0,1,2,3,4, find value of constant k

Deathfish, I have apparently misunderstood your problem. Tell me, are the numbers 0.4,0.1,0.1,0.1, and 0.3 you have listed above supposed to have been somehow given in the statement of the problem or they a result of your attempt at solving the problem? If they are results of your work they shouldn't be stated as part of the problem. If they are the result of your work, they are wrong as Halls has pointed out.
 
  • #5
0.4,0.1,0.1,0.1, and 0.3 are the values of P(x) in the question... values of x and corresponding P(x) are listed down in a table although i don't know how to post a table here... i have no idea what the question means by "If P(x)=k(5-x) for x = 0,1,2,3,4, find value of constant k" this i am copying down from the question too
 
  • #6
If P(x)= k(5- x), then it can not be the same P as for the given list.
 

FAQ: Probability distribution, find constant

1. What is a probability distribution?

A probability distribution is a mathematical function that describes the likelihood of a random variable taking on a certain value or set of values. It is often represented as a graph or table and can be used to calculate the probability of an event occurring within a given range.

2. How do you find the constant in a probability distribution?

The constant in a probability distribution is typically found by setting the sum of all probabilities equal to 1. This ensures that all possible outcomes are accounted for and the total probability is 100%. The constant can also be found by using the properties of the specific distribution, such as the mean and standard deviation, to calculate the value.

3. What is the difference between discrete and continuous probability distributions?

A discrete probability distribution deals with discrete or countable outcomes, such as the number of heads in a series of coin tosses. A continuous probability distribution deals with continuous outcomes, such as the height of a person. The constant in a discrete distribution represents the probability of a specific outcome, while in a continuous distribution it represents the area under the curve.

4. How do you interpret the constant in a probability distribution?

The constant in a probability distribution represents the likelihood of a specific outcome occurring. For example, if the constant is 0.25 in a discrete distribution, it means that there is a 25% chance of that outcome happening. In a continuous distribution, the constant represents the probability of the random variable falling within a certain range.

5. What are some common probability distributions used in statistics?

Some common probability distributions include the normal distribution, binomial distribution, Poisson distribution, and exponential distribution. Each distribution has its own properties and is used to model different types of data. The choice of distribution depends on the nature of the data and the research question being studied.

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