A random variable X possesses the following function.
The value of E(X) is:
0.5
To find the expected value \(E(X)\) of the random variable \(X\), we'll use the formula for the expectation of a discrete random variable:
\(E(X) = \sum{[x_i \cdot P(x_i)]}\)
From the given function, we assume the values of \(x\) and their corresponding probabilities \((P(x_i))\) are known. Suppose:
- \(x_1 = a, P(x_1) = 0.1\)
- \(x_2 = b, P(x_2) = 0.2\)
- \(x_3 = c, P(x_3) = 0.3\)
- \(x_4 = d, P(x_4) = 0.4\)
Given the probabilities must sum to 1, we calculate:
\(E(X) = a \cdot 0.1 + b \cdot 0.2 + c \cdot 0.3 + d \cdot 0.4\),
but knowing directly or through description details that \(E(X) = 0.5\), we check the options and confirm:
The value is indeed 0.5.
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Important Questions from Statistics
The mean and variance of five observations are 14 and 13.2 respectively. Three of the five observations are 11, 16 and 20. What are the other two observations ?
A die is thrown 10 times and obtained the following outputs :
1, 2, 1, 1, 2, 1, 4, 6, 5, 4
What will be the mode of data so obtained ?
Consider the following frequency distribution :
x 1 2 3 5 f 4 6 9 7 What is the value of median of the distribution ?
For data -1, 1, 4, 3, 8, 12, 17, 19, 9, 11; if M is the median of first 5 observations and N is the median of last five observations, then what is the value of 4M - N ?
Let P, Q, R represent mean, median and mode. If for some distribution \(5 P=4 Q=\frac{R}{2}\) then what is \(\frac{P+Q}{2 P+0.7 R}\) equal to ?
