The problem in the image seems to involve random variables $X$ and $Y$, where $X \sim N(3, 1)$ (normal distribution with mean 3 and variance 1), and $Y \sim B(5, 0.2)$ (binomial distribution with parameters 5 and probability 0.2). The goal is to compute the expected value of $U = E(XY + DX - \text{modX} \cdot \text{modY})$ and $DU$, as well as the probability $P(1 \leq X \leq 4)$.

To proceed:

1. Expected value of $U$: You need to calculate $E[U]$, using the properties of expectation and the given distributions for $X$ and $Y$.
2. Variance of $U$: $DU$ requires you to calculate the variance of $U$, which involves the second moments and covariance.
3. Probability: You are also asked to compute $P(1 \leq X \leq 4)$, which can be determined using the cumulative distribution function (CDF) for the normal distribution.

Would you like to proceed step by step on each part of the problem?