[Step-by-Step] Let X_1, X_2, ..., X_50 be an independent random sample of size 50 from Gamma (1,0.4). Let U be a random variable given by: U=∑_i=1^50
Question: Let \(X_{1}, X_{2}, \ldots, X_{50}\) be an independent random sample of size 50 from Gamma \((1,0.4)\).
- Let \(\mathrm{U}\) be a random variable given by:
- What is the distribution of \(\mathrm{U}\)
- Find the mean and the variance of the random variable \(\mathrm{U}\).
b) Use the Central Limit Theorem to find:
\[P\left(115 \leq \sum_{i=1}^{50} 5 X_{i} \leq 155\right)\]
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