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A random variable X takes the values -1,0,1 It mean is 0.6 ; if P(X=0)=0.2 Then P(X=1) is ?
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A random variable X takes the values -1,0,1 It mean is 0.6 ; if P(X=0)...
Understanding the Problem
To find P(X=1), we need to use the information given about the random variable X, which takes the values -1, 0, and 1. The mean (expected value) of X is 0.6, and we know that P(X=0) = 0.2.
Given Values
- Mean of X: 0.6
- P(X=0): 0.2
- Let P(X=-1) = p and P(X=1) = q
Probabilities Relationship
Since the probabilities must sum to 1, we have:
- P(X=-1) + P(X=0) + P(X=1) = 1
Substituting the known value:
- p + 0.2 + q = 1
- Thus, p + q = 0.8 (1)
Calculating the Mean
The expected value (mean) is calculated as follows:
- E(X) = (-1) * P(X=-1) + 0 * P(X=0) + 1 * P(X=1)
Substituting the known values:
- 0.6 = (-1) * p + 0 + 1 * q
- Thus, 0.6 = -p + q (2)
Solving the Equations
Now we have two equations:
1. p + q = 0.8
2. -p + q = 0.6
We can solve these equations simultaneously.
From equation (1):
- p = 0.8 - q
Substituting in equation (2):
- - (0.8 - q) + q = 0.6
- -0.8 + 2q = 0.6
- 2q = 1.4
- q = 0.7
Conclusion
Thus, we find:
- P(X=1) = q = 0.7
Therefore, P(X=1) is 0.7.
Community Answer
A random variable X takes the values -1,0,1 It mean is 0.6 ; if P(X=0)...
1.2
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A random variable X takes the values -1,0,1 It mean is 0.6 ; if P(X=0)=0.2 Then P(X=1) is ?
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