4) a) If X and Y are discrete random variable and k is a constant, then prove that. I. 𝐸(𝑋 + 𝐾) = 𝐸(𝑋) + 𝐾 II. 𝐸(𝑋 + 𝑌)
Posted: Sun Jul 10, 2022 11:45 am
4) a) If X and Y are discrete random variable and k is aconstant, then prove that.
I. 𝐸(𝑋 + 𝐾) = 𝐸(𝑋) + 𝐾
II. 𝐸(𝑋 + 𝑌) = 𝐸(𝑋) + 𝐸(𝑌)
b) The probability density function of the continuous randomvariable X,
𝑓𝑥(𝑋) = { 𝑘𝑒 − 𝑥/ 4, 0 ≤ 𝑥 ≤4
0, 𝑂/𝑊
I. Value of 𝑘
II. 𝐸(𝑋)
III. 𝑉𝑎𝑟(𝑋)
IV. 𝐹𝑥(𝑋)
V. 𝑃(𝑋 < 3|𝑋 > 2)
I. 𝐸(𝑋 + 𝐾) = 𝐸(𝑋) + 𝐾
II. 𝐸(𝑋 + 𝑌) = 𝐸(𝑋) + 𝐸(𝑌)
b) The probability density function of the continuous randomvariable X,
𝑓𝑥(𝑋) = { 𝑘𝑒 − 𝑥/ 4, 0 ≤ 𝑥 ≤4
0, 𝑂/𝑊
I. Value of 𝑘
II. 𝐸(𝑋)
III. 𝑉𝑎𝑟(𝑋)
IV. 𝐹𝑥(𝑋)
V. 𝑃(𝑋 < 3|𝑋 > 2)