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The probability density function of a continuous random variable is defined as follows: f(X) = c when -1≤x≤1= 0 , otherwise the value of c is a)1 b)-1 c)1/2 d)0 answer (c) . How?
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The probability density function of a continuous random variable is de...
Explanation:
The probability density function of a continuous random variable is defined as follows:

f(X) = c when -1≤x≤1= 0 , otherwise

To find the value of c, we need to use the property that the total area under the probability density function is equal to 1.

Step 1:
Write down the integral form of the total area under the probability density function.

∫f(x)dx = ∫-1^1 cdx + ∫(-∞,-1) 0 dx + ∫(1,∞) 0 dx

Step 2:
Simplify the integral by using the fact that the integral of a constant is equal to the constant times the length of the interval.

∫f(x)dx = c(1-(-1)) + 0 + 0 = 2c

Step 3:
Since the total area under the probability density function is equal to 1, we can set the integral equal to 1 and solve for c.

2c = 1

c = 1/2

Therefore, the value of c is 1/2.

Conclusion:
The answer is (c) 1/2.
Community Answer
The probability density function of a continuous random variable is de...
Integration of f(x) using limits= 1 .
then you will get the answer 1/2
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The probability density function of a continuous random variable is defined as follows: f(X) = c when -1≤x≤1= 0 , otherwise the value of c is a)1 b)-1 c)1/2 d)0 answer (c) . How?
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